Did you know that India has over 1 Lakh varieties of rice? That's right - more than 1,00,000 different types! Can you even imagine counting that many?
Large numbers are everywhere around us - from the grains of sand on a beach to the stars in the sky, from the population of our country to the money in a national budget. But how well do we really understand these numbers?
👦 Estu wonders:
How big IS a lakh, really? I mean, I know it's 1,00,000... but what does that actually FEEL like? Can you visualize it?
💡 Making Sense of a Lakh
⏱ 1 Lakh Seconds
= 1,00,000 seconds
= 1,666 minutes
= ~28 hours!
That's more than a full day!
🚶 1 Lakh Steps
= 1,00,000 steps
= roughly 80 km
That's Delhi to Agra on foot!
📚 1 Lakh Pages
= 1,00,000 pages
= about 400 textbooks
A whole library section!
🍞 1 Lakh Rotis
If you eat 4 rotis/day...
= ~68 years of rotis!
An entire lifetime of meals!
🌟 Fun Fact: India grows 1,00,000+ varieties of rice because of its diverse climate zones - from the cold Himalayan valleys to the tropical coast of Kerala. Farmers have been developing new varieties for thousands of years!
👧 Roxie:
Ready for an adventure? Let's travel through the Land of Tens and discover how numbers grow from hundreds to thousands to lakhs to crores! 🚀
📖 NCERT Figure it Out — Pages 2-3
🍚 Rice Varieties Explorer (Q1 & Q2)
India has 1,00,000 varieties of rice! Slide to change how many you taste per day.
2
Per Year
730
In 100 Years
73,000
vs 1 Lakh?
73% of 1 Lakh
Q2. If a person ate 3 varieties of rice every day, would they be able to taste all 1 lakh varieties in 100 years?
Solution:
Number of varieties tasted per day = 3
Number of days in 1 year = 365
Number of years = 100
Answer: Yes! They would taste 1,09,500 varieties, which is more than 1 lakh. They would be able to taste all 1 lakh varieties and still have room for 9,500 more!
Q3. According to the 2011 Census, the population of Chintamani town was about 75,000. How much less than one lakh is 75,000?
Solution:
One lakh = 1,00,000
Population of Chintamani = 75,000
Difference = 1,00,000 − 75,000
= 25,000
Answer: 75,000 is 25,000 (twenty-five thousand) less than one lakh.
Q4. The estimated population of Chintamani in 2024 is 1,06,000. How much more than one lakh is this?
Solution:
Estimated population in 2024 = 1,06,000
One lakh = 1,00,000
Difference = 1,06,000 − 1,00,000
= 6,000
Answer: The estimated population of 1,06,000 is 6,000 (six thousand) more than one lakh.
Q5. By how much did the population of Chintamani increase from 2011 to 2024?
Solution:
Population in 2011 = 75,000
Estimated population in 2024 = 1,06,000
Increase = 1,06,000 − 75,000
= 31,000
Answer: The population increased by 31,000 (thirty-one thousand) from 2011 to 2024.
🏢 Height to Floors Converter (Q6 & Q7)
How many building floors would match famous landmarks? Click a landmark or enter your own height!
Height (m)
÷
Floor Height (m)
=
Floors Needed
45
Statue of Unity
🌏2. Land of Tens
Join Roxie and Estu as they travel through the magical Land of Tens - where every new land is 10 times bigger than the last!
🏡 The Thoughtful Thousands (1,000s)
👦 Estu:
Welcome to Thousand-land! Here, everything comes in groups of 1,000. A thousand = 10 hundreds!
1 Thousand = 10 Hundreds = 1,000
A typical school has about 1,000 students
The highest denomination coin: Rs 1,000 note (discontinued, but we remember!)
A small Indian village has about 1,000 to 5,000 people
The Ramayana has about 24,000 verses (24 thousand)
There are about 28,000 railway stations in India
🤔 Think: 1 Thousand seconds = only about 16.7 minutes. You can count to a thousand in under 17 minutes!
🏆 The All-Powerful Lakhs (1,00,000s)
👧 Roxie:
Welcome to Lakh-land! This is where numbers get REALLY interesting. 1 Lakh = 100 Thousands = 1,00,000!
1 Lakh = 100 Thousands = 1,00,000
Cost of a good motorcycle: ~1 lakh rupees
Population of a small town: ~1-5 lakh
Shimla population: ~1.7 lakh
Hairs on your head: ~1 lakh!
There are about 6.38 lakh villages in India
😱 How long to count to 1 lakh? If you count 1 number per second without stopping: 1,00,000 seconds = ~28 hours non-stop! That's more than a full day of continuous counting!
👑 The Crore Commander (1,00,00,000s)
👦 Estu:
Whoa, Crore-land! This is the BIG league! 1 Crore = 100 Lakhs = 1,00,00,000. These are the numbers that run countries!
1 Crore = 100 Lakhs = 1,00,00,000
Population of Goa: ~15 lakh (a bit more than 1 crore... wait, less!)
Population of Delhi NCR: ~3 crore
A Bollywood blockbuster earns: 100-500 crore
India's population: ~144 crore!
If you earn Rs 1/second: 1 crore = ~3.8 months non-stop!
🔥 Scale ladder:
10 Ones = 1 Ten
10 Tens = 1 Hundred
10 Hundreds = 1 Thousand
10 Thousands = 1 Ten Thousand
10 Ten Thousands = 1 Lakh
10 Lakhs = 1 Ten Lakh
10 Ten Lakhs = 1 Crore
👧 Roxie:
So from Ones to Crore, we multiply by 10 exactly 7 times! 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,00,00,000. That's the beauty of our number system!
📖 NCERT Figure it Out — Pages 5-7
In the NCERT textbook, there are special calculators with only one button each. Let's figure out how many button presses are needed!
🔢 Try the NCERT Calculator!
Pick a calculator type, then try to reach the target number!
Q16. Write 2 different ways to make 8,300 using the buttons +1, +10, +100, and +1000.
Solution: Way 1: Press +1000 eight times, then +100 three times
= 8 × 1000 + 3 × 100 = 8,000 + 300 = 8,300 ✔
Total button clicks = 8 + 3 = 11 clicks
Way 2: Press +100 eighty-three times
= 83 × 100 = 8,300 ✔
Total button clicks = 83 clicks
Way 1 is much more efficient!
Q17. Write 2 different ways to make 40,629 using the buttons +1, +10, +100, and +1000.
Solution: Way 1 (place-value method):
Press +1000 forty times = 40 × 1000 = 40,000
Press +100 six times = 6 × 100 = 600
Press +10 two times = 2 × 10 = 20
Press +1 nine times = 9 × 1 = 9
Total = 40,000 + 600 + 20 + 9 = 40,629 ✔
Total clicks = 40 + 6 + 2 + 9 = 57 clicks
Way 2:
Press +1000 forty times = 40,000
Press +10 sixty-two times = 620
Press +1 nine times = 9
Total = 40,000 + 620 + 9 = 40,629 ✔
Total clicks = 40 + 62 + 9 = 111 clicks
Q18. For the number 66,666, what is the MINIMUM number of button clicks needed?
Solution:
To minimise clicks, use the largest button possible for each place value:
Ten-thousands digit: 6 → Press +1000 sixty times? No! We need to think in terms of available buttons.
Since the largest button is +1000:
Press +1000 sixty-six times = 66,000 (66 clicks)
Press +100 six times = 600 (6 clicks)
Press +10 six times = 60 (6 clicks)
Press +1 six times = 6 (6 clicks)
Wait — but 66 = 6 × 11, so we can also think of it as:
The minimum number of clicks = sum of what each digit contributes when using the highest-value button for each position.
Since the highest button is +1000, the ten-thousands place (6) requires 60 presses of +1000, and the thousands place (6) requires 6 more presses of +1000.
Key insight: With buttons +1, +10, +100, +1000, the minimum clicks for any number equals: (ten-thousands digit × 10 + thousands digit) for the +1000 button, plus hundreds digit for +100, plus tens digit for +10, plus ones digit for +1.
Q19. "The minimum number of button clicks to reach a number (up to 9,999) equals the sum of its digits." Why is this true?
Solution:
Consider a 4-digit number like 4,527:
Using the optimal strategy (each digit uses its matching place-value button):
Thousands digit (4): Press +1000 four times → 4 clicks
Hundreds digit (5): Press +100 five times → 5 clicks
Tens digit (2): Press +10 two times → 2 clicks
Ones digit (7): Press +1 seven times → 7 clicks
Total clicks = 4 + 5 + 2 + 7 = 18 = sum of digits ✔
Why it works: Each digit tells you exactly how many times to press that place-value button. The thousands digit says how many thousands, the hundreds digit says how many hundreds, and so on. Since we have a button for each place value (+1, +10, +100, +1000), each digit directly becomes the number of presses for its button. So the total presses = sum of all digits!
Note: This works perfectly for numbers up to 9,999 (4 digits). For larger numbers like 66,666, the ten-thousands digit has no matching button, so extra presses of +1000 are needed.
📑3. Reading Large Numbers
Reading large numbers correctly is super important. India and many Western countries use different systems to organize digits. Let's master both!
🇮🇳 Indian Place Value System
Place
Crores
Ten Lakhs
Lakhs
Ten Thousands
Thousands
Hundreds
Tens
Ones
Value
1,00,00,000
10,00,000
1,00,000
10,000
1,000
100
10
1
Zeros
7
6
5
4
3
2
1
0
✏ Indian Comma Rules
Step 1: Start from the right. Place the first comma after 3 digits (separates hundreds from thousands). Step 2: After that, place a comma every 2 digits.
Example: 98345612 becomes 9,83,45,612
Read as: Nine crore eighty-three lakh forty-five thousand six hundred twelve
🌎 International Place Value System
Place
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
Value
100,000,000
10,000,000
1,000,000
100,000
10,000
1,000
100
10
1
International commas: Place a comma every 3 digits from the right. Example: 98345612 becomes 98,345,612
Read as: Ninety-eight million three hundred forty-five thousand six hundred twelve
🔄 Indian vs International Comparison
Indian System
= International System
Number
1 Thousand
1 Thousand
1,000
1 Lakh
100 Thousand
1,00,000
10 Lakh
1 Million
10,00,000
1 Crore
10 Million
1,00,00,000
10 Crore
100 Million
10,00,00,000
100 Crore
1 Billion
1,00,00,00,000
👧 Roxie:
Remember: 1 Million = 10 Lakh and 1 Billion = 100 Crore. These are the two most important conversions!
📝 Worked Example
Let's read 9,83,45,612 in both systems:
🇮🇳 Indian System
9,83,45,612
Nine crore eighty-three lakh forty-five thousand six hundred twelve
🌎 International System
98,345,612
Ninety-eight million three hundred forty-five thousand six hundred twelve
💭 Memory Trick: Indian system: "3-2-2-2" pattern (3 digits, then groups of 2). International system: "3-3-3-3" pattern (always groups of 3).
📖 NCERT Figure it Out — Pages 4-5
Q1. Write in words (Indian system): 3,00,600
Solution:
Break the number using Indian place values:
Tip: Be careful with the zeros! There are zeros in the lakh place and the hundreds place.
Q8. Write in numerals: "Ten lakh two hundred thirty-five"
Solution:
Break it down piece by piece:
Ten lakh = 10,00,000
Two hundred thirty-five = 235
(Note: there are zero thousands and zero ten-thousands!)
Total = 10,00,000 + 235
Answer: 10,00,235
Tip: When there is no "thousand" part mentioned, those places get zeros. The number has zeros in both the ten-thousands and thousands places.
🇮🇳4. Of Crores and Crores!
Let's explore some mind-boggling real-world numbers from India and the world!
🇮🇳 India's Population
~1,44,00,00,000
144 Crore
= 1.44 Billion
🌎 World Population
~8,00,00,00,000
800 Crore
= 8 Billion
🏛 Uttar Pradesh
~24,00,00,000
24 Crore
Most populous state!
🏛 Maharashtra
~13,00,00,000
13 Crore
2nd most populous
🏝 Goa
~15,00,000
15 Lakh
Smallest state by population!
💰 India's GDP
~Rs 272,00,00,00,00,000
~Rs 272 Lakh Crore
= ~$3.5 Trillion
💵 RBI Currency Notes
Total currency in circulation:
~Rs 34 Lakh Crore
That's a LOT of paper money!
🚋 Indian Railways
Passengers per day:
~2.3 Crore
= 23 Million daily!
👦 Estu:
India's population of 144 crore means if you counted 1 person per second, it would take you over 456 years to count everyone! 😲
📖 NCERT Figure it Out — Page 9
City
2001 Population
2011 Population
Mumbai
1,19,78,450
1,24,42,373
Delhi
98,17,439
1,10,07,835
Bengaluru
43,01,326
84,25,970
Hyderabad
36,37,483
68,09,970
Pune
25,38,473
31,15,431
Surat
24,33,835
44,67,797
Q1. Write 48,121,620 in words in both the Indian system and the International system.
Solution:
Step 1 — Indian system:
Place commas the Indian way (3-2-2 from right): 4,81,21,620
Read: Four crore eighty-one lakh twenty-one thousand six hundred twenty.
Step 2 — International system:
Place commas the International way (groups of 3 from right): 48,121,620
Read: Forty-eight million one hundred twenty-one thousand six hundred twenty.
Q2. Write 246,813,579 in words in both the Indian system and the International system.
Solution:
Step 1 — Indian system:
Place commas the Indian way: 24,68,13,579
Read: Twenty-four crore sixty-eight lakh thirteen thousand five hundred seventy-nine.
Step 2 — International system:
Place commas the International way: 246,813,579
Read: Two hundred forty-six million eight hundred thirteen thousand five hundred seventy-nine.
Q3. Write in numerals: "One crore one lakh one thousand ten"
Solution:
Break it down piece by piece:
One crore = 1,00,00,000
One lakh = 1,00,000
One thousand = 1,000
Ten = 10
Answer: Both Bengaluru (43 lakh → 84 lakh, ratio 1.96) and Surat (24 lakh → 44 lakh, ratio 1.84) nearly doubled their populations from 2001 to 2011. Bengaluru came the closest to exactly doubling.
Q9. By how much did Delhi's population increase from 2001 to 2011?
Solution:
Delhi's population in 2001 = 98,17,439
Delhi's population in 2011 = 1,10,07,835
Increase = 1,10,07,835 − 98,17,439
Let's subtract step by step:
1,10,07,835
− 98,17,439
___________
11,90,396
Answer: Delhi's population increased by 11,90,396 (eleven lakh ninety thousand three hundred ninety-six) from 2001 to 2011. That is nearly 12 lakh more people in just 10 years!
Q10. Round Mumbai's 2011 population (1,24,42,373) to the nearest lakh.
Solution:
Mumbai's 2011 population = 1,24,42,373
To round to the nearest lakh, we look at the ten-thousands digit:
1,24,42,373
The ten-thousands digit is 4.
Since 4 < 5, we round down.
Replace all digits after the lakh place with zeros.
Remember the rhyme: "4 or less, let it rest!" — the 24 lakhs stays as 24 lakhs.
🎯5. Exact and Approximate Values
Not all numbers we use are exact. Sometimes we use exact values and sometimes approximate values. Let's understand when to use each!
✅ Exact Values
Your marks in an exam: 87
Students in your class: 42
Pages in your textbook: 168
Your bank balance: Rs 12,543
Days in a year: 365
Players in a cricket team: 11
Approximate Values
India's population: ~144 crore
Stars in the sky: thousands of crores
Crowd at a rally: ~5 lakh
Grains of sand on a beach: crores
Distance to Sun: ~15 crore km
Cells in your body: ~37 lakh crore
📈 When to Use What?
Situation
Type
Why?
Your exam score
Exact
Every mark matters!
Crowd at a cricket match
Approximate
Impossible to count exactly
Money in your piggy bank
Exact
You can count every coin
Number of fish in the ocean
Approximate
Can't count them all!
Students in your school
Exact
School records are precise
Population of a city
Approximate
People are born/die every minute
👧 Roxie:
Key insight: When numbers are very large or constantly changing, we use approximate values. When we need precision (like money or scores), we use exact values!
📊6. Nearest Neighbours (Rounding)
Rounding helps us simplify numbers. It's like finding the nearest "friendly" number!
🌟 The Golden Rule of Rounding:
Look at the digit to the RIGHT of the place you're rounding to:
🟢 5 or more - Round UP! ("5 or more, raise the score!")
🔴 Less than 5 - Round DOWN! ("4 or less, let it rest!")
🎯 Round to Nearest 10
23 → 20
3 < 5, so round down
87 → 90
7 >= 5, so round up
155 → 160
5 >= 5, so round up
44 → 40
4 < 5, so round down
🎯 Round to Nearest 100
823 → 800
Tens digit is 2 (< 5), round down
2,567 → 2,600
Tens digit is 6 (>= 5), round up
1,450 → 1,500
Tens digit is 5 (>= 5), round up
9,349 → 9,300
Tens digit is 4 (< 5), round down
🎯 Round to Nearest 1,000
4,325 → 4,000
Hundreds digit is 3 (< 5)
7,891 → 8,000
Hundreds digit is 8 (>= 5)
🎯 Round to Nearest Lakh
3,45,678 → 3,00,000
Ten thousands digit is 4 (< 5)
3,65,678 → 4,00,000
Ten thousands digit is 6 (>= 5)
🎯 Round to Nearest Crore
4,56,78,123 → 5,00,00,000
Ten lakhs digit is 5 (>= 5), round up!
2,34,56,789 → 2,00,00,000
Ten lakhs digit is 3 (< 5), round down
💭 Memory Rhyme:
"5 or more, raise the score. 4 or less, let it rest!"
🎯 Animated Rounding Explorer
Enter any number and watch it round to different place values on the number line!
📖 NCERT Figure it Out — Page 10-11
Q1. Find the 5 nearest neighbours of 3,87,69,957.
Solution:
We round 3,87,69,957 to different place values:
Nearest Thousand: Look at the hundreds digit (9). Since 9 ≥ 5, round up.
3,87,69,957 → 3,87,70,000
Nearest Ten Thousand: Look at the thousands digit (9). Since 9 ≥ 5, round up.
3,87,69,957 → 3,87,70,000
Nearest Lakh: Look at the ten-thousands digit (6). Since 6 ≥ 5, round up.
3,87,69,957 → 3,88,00,000
Nearest Ten Lakh: Look at the lakhs digit (7). Since 7 ≥ 5, round up.
3,87,69,957 → 3,90,00,000
Nearest Crore: Look at the ten-lakhs digit (8). Since 8 ≥ 5, round up.
3,87,69,957 → 4,00,00,000
Q2. Find the 5 nearest neighbours of 29,05,32,481.
Solution:
We round 29,05,32,481 to different place values:
Nearest Thousand: Look at the hundreds digit (4). Since 4 < 5, round down.
29,05,32,481 → 29,05,32,000
Nearest Ten Thousand: Look at the thousands digit (2). Since 2 < 5, round down.
29,05,32,481 → 29,05,30,000
Nearest Lakh: Look at the ten-thousands digit (3). Since 3 < 5, round down.
29,05,32,481 → 29,05,00,000
Nearest Ten Lakh: Look at the lakhs digit (5). Since 5 ≥ 5, round up.
29,05,32,481 → 29,10,00,000
Wait — let us re-check. The lakhs digit is 0 and the ten-thousands digit is 3. For nearest ten lakh, we look at the lakhs digit (5). Actually, the number is 29,05,32,481. Breaking it down: 29 crore, 05 lakh, 32 thousand, 481. The lakhs digit is 5. Since 5 ≥ 5... but actually the digit in the lakhs place is 0, and we look at the next digit (ten-thousands = 3). Since 3 < 5, round down.
29,05,32,481 → 29,00,00,000
Nearest Crore: Look at the ten-lakhs digit (0). Since 0 < 5, round down.
29,05,32,481 → 29,00,00,000
Q3. "I have a number for which all five nearest neighbours (nearest thousand, ten thousand, lakh, ten lakh, and crore) are 5,00,00,000. What could the number be?"
Solution:
The number must round to 5,00,00,000 at every level — thousand, ten thousand, lakh, ten lakh, and crore.
Step 1: For nearest crore = 5,00,00,000, the number must be between 4,50,00,000 and 5,49,99,999. Step 2: For nearest ten lakh = 5,00,00,000, the number must be between 4,95,00,000 and 5,04,99,999. Step 3: For nearest lakh = 5,00,00,000, the number must be between 4,99,50,000 and 5,00,49,999. Step 4: For nearest ten thousand = 5,00,00,000, the number must be between 4,99,95,000 and 5,00,04,999. Step 5: For nearest thousand = 5,00,00,000, the number must be between 4,99,99,500 and 5,00,00,499.
The tightest range is 4,99,99,500 to 5,00,00,499.
Any number in this range works! For example: 5,00,00,000 or 4,99,99,873 or 5,00,00,321.
There are 1,000 such numbers (from 4,99,99,500 to 5,00,00,499 inclusive).
Q4. Estimate 4,63,128 + 4,19,682 by rounding each number to the nearest lakh and adding. What is the exact sum? How close is your approximation?
Solution: Estimation (rounding to nearest lakh):
4,63,128 → 5,00,000 (ten-thousands digit is 6 ≥ 5, round up)
4,19,682 → 4,00,000 (ten-thousands digit is 1 < 5, round down)
Estimated sum = 5,00,000 + 4,00,000 = 9,00,000
Exact sum:
4,63,128 + 4,19,682 = 8,82,810
Comparison:
Difference = 9,00,000 − 8,82,810 = 17,190
The approximation of 9,00,000 is quite close to the exact answer of 8,82,810. The estimation is off by only about 2% — pretty good for a quick mental calculation!
Q5. Estimate 14,63,128 − 4,90,020 by rounding each number to the nearest lakh. What is the exact difference?
Comparison:
The estimate of 10,00,000 is close to the exact answer of 9,73,108.
Difference = 10,00,000 − 9,73,108 = 26,892
The estimation overshoots by about 2.8% — still a useful quick approximation!
Q6. Round the number 67,385 to the nearest 10, nearest 100, nearest 1,000, and nearest 10,000.
Solution:
Number: 67,385
Nearest 10: Look at the ones digit (5). Since 5 ≥ 5, round up.
67,385 → 67,390
Nearest 100: Look at the tens digit (8). Since 8 ≥ 5, round up.
67,385 → 67,400
Nearest 1,000: Look at the hundreds digit (3). Since 3 < 5, round down.
67,385 → 67,000
Nearest 10,000: Look at the thousands digit (7). Since 7 ≥ 5, round up.
67,385 → 70,000
🔢7. Patterns in Products (Powers of 10)
When we multiply 10 by itself, a beautiful pattern emerges!
Expression
Calculation
Result
Number of Zeros
101
10
10
1
102
10 x 10
100
2
103
10 x 10 x 10
1,000
3
104
10 x 10 x 10 x 10
10,000
4
105
10 x 10 x 10 x 10 x 10
1,00,000 (1 Lakh)
5
106
10 x ... (6 times)
10,00,000 (10 Lakh)
6
107
10 x ... (7 times)
1,00,00,000 (1 Crore)
7
108
10 x ... (8 times)
10,00,00,000
8
109
10 x ... (9 times)
1,00,00,00,000 (100 Crore)
9
1012
10 x ... (12 times)
1,00,00,00,00,00,000
12
👧 Roxie:
See the pattern? The power tells you the number of zeros!
105 = 1 followed by 5 zeros = 1,00,000
💡 Multiplying by Powers of 10
When you multiply any number by a power of 10, just add that many zeros!
5 x 103
= 5 x 1,000
= 5,000
(Add 3 zeros to 5)
7 x 105
= 7 x 1,00,000
= 7,00,000
(Add 5 zeros to 7)
23 x 104
= 23 x 10,000
= 2,30,000
(Add 4 zeros to 23)
15 x 107
= 15 x 1,00,00,000
= 15,00,00,000
(Add 7 zeros to 15)
101
10
Ten
102
100
Hundred
103
1,000
Thousand
104
10,000
Ten Thousand
105
1,00,000
Lakh
106
10,00,000
Ten Lakh / Million
107
1,00,00,000
Crore
109
1,00,00,00,000
100 Crore / Billion
1012
1,00,00,00,00,00,000
Lakh Crore / Trillion
💭 Memory: "The power = number of zeros." Simple!
📖 NCERT Figure it Out — Page 14-15
Q1. Calculate: 735 × 10, 735 × 100, 735 × 1000. What pattern do you see?
Pattern: When you multiply a number by 10, 100, or 1,000, you simply add 1, 2, or 3 zeros to the end of the number respectively. In general, multiplying by 10n adds n zeros to the number!
Q2. Roxie says the product of two 2-digit numbers can only be a 3-digit or 4-digit number. Is she correct? Verify.
Solution: Yes, Roxie is correct!
Smallest product of two 2-digit numbers:
10 × 10 = 100 → This is a 3-digit number.
Largest product of two 2-digit numbers:
99 × 99 = 9,801 → This is a 4-digit number.
Since the smallest product gives 3 digits and the largest gives 4 digits, the product of any two 2-digit numbers will always be either a 3-digit or 4-digit number. ✅
Q3. What about the product of a 2-digit and a 3-digit number? How many digits can it have?
Solution: Smallest product:
10 × 100 = 1,000 → This is a 4-digit number.
Largest product:
99 × 999 = 98,901 → This is a 5-digit number.
So the product of a 2-digit number and a 3-digit number can be either a 4-digit or 5-digit number.
Q4. If a number with m digits is multiplied by a number with n digits, the product has at most m+n digits and at least m+n−1 digits. Verify with: (a) 23 × 456 and (b) 99 × 9.
Solution: (a) 23 × 456:
m = 2 digits, n = 3 digits
Maximum possible digits = m + n = 2 + 3 = 5
Minimum possible digits = m + n − 1 = 2 + 3 − 1 = 4
Actual product: 23 × 456 = 10,488 → 5 digits ✅
5 is between 4 and 5 (min and max). Rule verified!
(b) 99 × 9:
m = 2 digits, n = 1 digit
Maximum possible digits = m + n = 2 + 1 = 3
Minimum possible digits = m + n − 1 = 2 + 1 − 1 = 2
Actual product: 99 × 9 = 891 → 3 digits ✅
3 is between 2 and 3 (min and max). Rule verified!
Q5. Multiplication shortcut: Calculate 116 × 5 using the trick of multiplying by 10 and dividing by 2.
Solution: Trick: Multiplying by 5 is the same as multiplying by 10 and dividing by 2 (since 5 = 10 ÷ 2).
Step 1: 116 × 10 = 1,160
Step 2: 1,160 ÷ 2 = 580
Therefore, 116 × 5 = 580
Why this works: 5 = 10/2, so a × 5 = a × 10/2. Multiplying by 10 is easy (just add a zero), and dividing by 2 is easy (just halve it)!
Q6. Calculate 824 × 25 using the trick of multiplying by 100 and dividing by 4.
Solution: Trick: Multiplying by 25 is the same as multiplying by 100 and dividing by 4 (since 25 = 100 ÷ 4).
Why this works: 25 = 100/4, so a × 25 = a × 100/4. Multiplying by 100 is easy (add two zeros), and dividing by 4 is easy (halve it twice)!
Q7. Calculate 125 × 40 × 8 × 25. Hint: group the numbers cleverly!
Solution: Trick: Look for pairs that multiply to give round numbers!
Rearrange: (125 × 8) × (40 × 25)
Group 1: 125 × 8 = 1,000 💡 Group 2: 40 × 25 = 1,000 💡
Now: 1,000 × 1,000 = 10,00,000 (Ten Lakh!)
Key insight: Clever grouping turns a complex multiplication into a simple one! Always look for pairs like 125×8=1000, 25×4=100, 50×2=100, etc.
🫀8. Did You Ever Wonder? (Body Numbers)
Your body is a number factory! Let's calculate some amazing numbers about the human body.
❤ Heartbeats
~72 beats/minute
Per day: 72 x 60 x 24 = 1,03,680
Per year: 1,03,680 x 365 = 3,78,43,200
In 75 years: ~283 crore (nearly 3 billion!)
👁 Eye Blinks
~15 blinks/minute
Per day: 15 x 60 x 16 = 14,400
(Assuming 16 waking hours)
Per year: 52,56,000
🌅 Breaths
~15 breaths/minute
Per day: 15 x 60 x 24 = 21,600
Per year: 78,84,000
In lifetime: ~59 crore!
💇 Hair on Head
Average: ~1,00,000
That's 1 Lakh hairs!
You lose ~50-100 per day
🧬 Cells in Body
~37,00,00,00,00,00,000
= 37 Lakh Crore
= 37 Trillion cells!
🩸 Blood
Total blood: ~5 litres
Heart pumps: ~7,500 litres/day!
That's 1,500 times your total blood volume daily
👦 Estu:
My heart will beat about 283 crore times in my life! That's almost 3 billion beats - and I don't even have to think about it!
🛰9. Distances Around Us
From city to city to planet to star - distances keep getting larger and larger!
🚌 Mumbai to Delhi
~1,400 km
By road: ~24 hours drive
🚌 Delhi to Chennai
~2,180 km
Almost across India!
🌎 Earth's Diameter
12,742 km
Distance through Earth's center
🌎 Earth's Circumference
40,075 km
Distance around the Earth
🌔 Earth to Moon
3,84,400 km
~3.84 Lakh km
Chandrayaan-3 covered this!
☀ Earth to Sun
15,00,00,000 km
= 15 Crore km!
Light takes 8 min 20 sec
⚡ Speed of Light
3,00,000 km/sec
= 3 Lakh km per second!
Fastest speed possible
⭐ Nearest Star
(Proxima Centauri)
~4.24 light years
= ~40,00,00,00,00,000 km
= ~40 Lakh Crore km!
👧 Roxie:
The nearest star is 40 lakh crore km away! Even light, which travels at 3 lakh km per second, takes 4.24 years to get there. Space is UNIMAGINABLY vast!
💡 What is a Light Year? It's the distance light travels in 1 year. Speed of light = 3,00,000 km/s. So 1 light year = 3,00,000 x 60 x 60 x 24 x 365 = ~9.46 x 1012 km (about 9.46 lakh crore km!)
📖 NCERT Figure it Out — Page 16-19
Q1. Can Roxie reach the Moon if she travels 100 km every day for 10 years? (Distance to the Moon = 3,84,400 km)
Solution: Distance Roxie can cover in 10 years:
Days in 10 years = 365 × 10 = 3,650 days
Distance covered = 100 × 3,650 = 3,65,000 km
Distance to Moon = 3,84,400 km
Since 3,65,000 < 3,84,400, No! Roxie cannot reach the Moon.
She falls short by 3,84,400 − 3,65,000 = 19,400 km.
She would need about 10 years and 194 more days (roughly 10.5 years) at 100 km/day to reach the Moon!
Q2. Can you reach the Sun in a lifetime if you travel 1,000 km every day? (Earth-Sun distance = 14,70,00,000 km)
Years needed to reach the Sun:
14,70,00,000 ÷ 3,65,000 ≈ 403 years!
Not possible in a lifetime! Even at 1,000 km per day (that is faster than a typical airplane!), it would take about 403 years to reach the Sun. A human lifetime is only about 75-80 years. This shows just how incredibly far the Sun is from Earth.
Q3. If 1 sheet of paper weighs 5 grams, could you lift 1 lakh sheets?
Number of Titanics needed = 1,24,00,000 ÷ 2,500
= 4,960 ships!
You would need 4,960 Titanics to carry all of Mumbai's population! That is nearly 5 thousand ships. This really puts into perspective how large a city's population is compared to even the biggest ships ever built.
Q6. A bar-tailed godwit (a bird) flew 13,560 km non-stop in 11 days. How much distance did it cover per day? Per hour?
Distance per hour:
1,233 ÷ 24 ≈ 51 km/hour (approximately)
That is remarkable! This small bird flew at an average speed of about 51 km/hour without stopping for 11 straight days. It is one of the longest non-stop flights in the animal kingdom, flying from Alaska to New Zealand across the Pacific Ocean!
📝10. Cooking Up Problems
Let's solve some real-world word problems using large numbers!
Q1. A factory makes 8,750 toys per day. How many toys in 1 year (365 days)?
Solution:
Toys per day = 8,750
Toys in 1 year = 8,750 x 365
= 31,93,750
= Thirty-one lakh ninety-three thousand seven hundred fifty toys!
Q2. If you save Rs 15 per day, how much do you save in 1 year? In 20 years?
Solution:
Per year: 15 x 365 = Rs 5,475
In 20 years: 5,475 x 20 = Rs 1,09,500 (over 1 lakh!)
Just Rs 15/day makes you a lakhpati in 20 years!
Q3. A cricket stadium seats 1,32,000 people. If each ticket costs Rs 500, what is the total collection?
Solution:
Total collection = 1,32,000 x 500
= 6,60,00,000
= Rs 6.6 Crore!
Q4. India has ~6,38,000 villages. If each village has ~1,000 people, what is the total rural population?
Solution:
Total = 6,38,000 x 1,000
= 63,80,00,000
= 63.8 Crore people living in villages!
Q5. An IPL match has 50 lakh viewers online. If there are 3 matches/week for 8 weeks, what are total views?
Solution:
Total matches = 3 x 8 = 24 matches
Total views = 50,00,000 x 24
= 12,00,00,000
= 12 Crore views!
Q6. A school library has 12,500 books. If the school plans to add 750 books every year, how many books will there be after 10 years?
Solution:
Books added in 10 years = 750 x 10 = 7,500
Total = 12,500 + 7,500 = 20,000 books (Twenty thousand)
Q7. Mumbai local trains carry 75,00,000 passengers daily. How many passengers in a month (30 days)?
Q8. A farmer harvests 2,400 kg of wheat from 1 hectare. If he has 35 hectares, how much total wheat?
Solution:
Total wheat = 2,400 x 35
= 84,000 kg = 84 tonnes of wheat!
Q9. Earth to Moon is 3,84,400 km. If a spacecraft travels at 1,000 km/hour, how many hours to reach the Moon?
Solution:
Time = Distance / Speed = 3,84,400 / 1,000
= 384.4 hours
= approximately 16 days!
Q10. India produces about 3,10,00,000 tonnes of food grains per year. If equally distributed among 144 crore people, how much does each person get per year?
Solution:
3,10,00,000 tonnes = 31,00,00,00,00,000 grams (31 lakh crore grams)
Per person = 31,00,00,00,00,000 / 1,44,00,00,000
= approximately 215 kg per person per year
= about 590 grams per day
🧩Mix Questions (NCERT)
These challenging problems from the NCERT textbook combine multiple concepts. Try them!
Q1. Using digits 0-9 each exactly once (the first digit cannot be 0), write the largest 10-digit number that is a multiple of 5.
Solution: Key constraints:
• Must use each digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) exactly once.
• First digit cannot be 0.
• Must be a multiple of 5 (so the last digit must be 0 or 5).
Strategy: To make the largest number, place the biggest digits first. To be a multiple of 5, the last digit must be 0 or 5. To maximize the number, we should put 0 at the end (not 5), so the higher digits stay in front.
Arrange remaining digits (9, 8, 7, 6, 5, 4, 3, 2, 1) in descending order, then put 0 at the end:
Q2. Using digits 0-9 each exactly once, write the smallest even 10-digit number.
Solution: Key constraints:
• Must use each digit (0-9) exactly once.
• First digit cannot be 0 (must be a valid 10-digit number).
• Must be even (last digit must be 0, 2, 4, 6, or 8).
Strategy: To make the smallest 10-digit number, the first digit should be 1 (smallest non-zero digit). Then arrange remaining digits in ascending order, but the last digit must be even.
Start with 1. Remaining digits: 0, 2, 3, 4, 5, 6, 7, 8, 9.
Place 0 next (smallest available), then ascending: 2, 3, 4, 5, 6, 7...
But the last digit must be even. If we place digits as 1, 0, 2, 3, 4, 5, 6, 7, 9, 8 — the last digit is 8 (even!) and we swap 8 and 9 to keep it small.
Q3. Write a 9-digit number where swapping any two digits makes it bigger.
Solution: Think about it: If swapping any two digits makes the number bigger, then the number must already be the smallest possible arrangement of its digits.
This means the digits must be in non-decreasing order (ascending order from left to right).
Example 1:10,00,00,000 (Ten Crore)
Digits: 1, 0, 0, 0, 0, 0, 0, 0, 0. Any swap either keeps it the same or makes it bigger.
Example 2:12,34,56,789
Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9. Digits are in ascending order. Swapping any two would put a larger digit earlier, making the number bigger.
Example 3:11,11,11,111
All digits are the same, so any swap produces the same number (or we can say it does not get smaller).
Q4. A calculator has only two buttons: "+10,000" and "+100". Starting from 0, how many button presses are needed to reach: (a) 20,800 (b) 92,100 (c) 1,20,500?
Number of crores in a billion = 1,00,00,00,000 ÷ 1,00,00,000
= 100 crore
So, 100 crore = 1 billion.
This is one of the most important conversions to remember!
Q7. A sheet of paper is about 0.1 mm thick. How many sheets stacked would match the height of the Statue of Unity (180 m)?
Solution: Convert to same units:
Height of Statue of Unity = 180 m = 180 × 1,000 mm = 1,80,000 mm
Thickness of one sheet = 0.1 mm
Number of sheets needed:
1,80,000 ÷ 0.1 = 18,00,000 sheets
That is 18 lakh sheets of paper!
If a ream (500 sheets) costs about Rs 300, you would need 3,600 reams costing Rs 10,80,000 (over 10 lakh rupees!) just to match the height of the statue!
Q8. The great composer Purandaradasa composed 4,75,000 songs over 65 years. How many songs per year? How many songs per day?
Solution: Songs per year:
4,75,000 ÷ 65 ≈ 7,308 songs per year (approximately)
Songs per day:
7,308 ÷ 365 ≈ 20 songs per day!
That is truly astounding — Purandaradasa composed about 20 songs every single day for 65 years! He is rightly called the "Pitamaha" (father) of Carnatic music. This shows the incredible dedication and genius of Indian classical musicians.
Q9. Express 2,100 × 70,000 in both Indian and International notation. Write in words in both systems.
Indian notation: 14,70,00,000 In words: Fourteen crore seventy lakh
International notation: 147,000,000 In words: One hundred forty-seven million
Equivalence: 14 crore 70 lakh = 147 million
Q10. India produces about 52,00,00,00,000 kg of plastic waste. If shared among 130 crore (1,30,00,00,000) people, how much plastic waste per person?
Solution: Total plastic waste: 52,00,00,00,000 kg Population: 1,30,00,00,000 people
Plastic waste per person:
52,00,00,00,000 ÷ 1,30,00,00,000
= 5200 ÷ 130
= 40 kg per person!
Every person in India is responsible for about 40 kg of plastic waste. That is roughly the weight of a medium-sized suitcase full of plastic! This highlights why reducing plastic use is so important for our environment.
🎮Interactive Games & Tools
🔢 Live Number Reader
Type any number up to 12 digits and see it formatted + spoken in words!
Indian Format
—
International Format
—
Type a number above
🔴 Lakh Dot Visualizer
See how big 1 Lakh really is! Add dots and try to reach 1,00,000!
Dots: 0
🎲 Place Value Explorer
A random number appears. Watch digits fill the chart, then answer the quiz!
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Crores
-
Ten Lakhs
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Lakhs
-
Ten Th.
-
Thousands
-
Hundreds
-
Tens
-
Ones
-
⚔ Number Battle
Two numbers appear - click the BIGGER one! How many can you get right?
✅ 0❌ 0🔥 Streak: 0
?
VS
?
🤔 Estimation Challenge
Guess how many dots are on the grid. How close can you get?
Your guess:
📰 Newspaper Number Hunt
Click on the numbers in these headlines to see them explained!
The Daily Numbers
Sensex Crosses 78,500 Mark -- Investors Gain Rs 4.5 Lakh Crore
IPL 2024 Final Watched by 3,20,00,000 Viewers Online
India's Population Reaches 1,44,17,24,000
Chandrayaan-3 Travelled 3,84,400 km to Reach Moon
Mumbai Local Carries 75,00,000 Passengers Daily
🫀 Body Numbers Calculator
Enter your heartbeat rate and see how many times your heart beats!
❤Per Hour
4,320
🌃Per Day
1,03,680
📅Per Year
3,78,43,200
🌟In 75 Years
2,83,82,40,000
~284 Crore
🛰 Distance Comparison Tool
Click any two distances to compare them visually!
🚌Mumbai-Delhi1,400 km
🚌Delhi-Chennai2,180 km
🌎Earth Diameter12,742 km
🌎Earth Circumf.40,075 km
🌔Earth-Moon3,84,400 km
☀Earth-Sun15 Crore km
Select two distances to compare
🇮🇳 State Population Match
Match each state with its population! Click a state, then click its population.
Matched: 0/8
States
Population
🔢 NCERT Calculator Activity
A calculator with limited buttons! Can you reach the target number? Try using minimum clicks!
Target:--
0
Clicks: 0Minimum: --
🎯 Rounding Practice Game
Round the number to the given place. Pick the correct answer!
✅ 0❌ 0
Round to nearest...
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📚Practice Questions
🎯 Multiple Choice Questions (20 MCQs)
1. How many zeros are there in 1 Crore?
a) 5
b) 7
c) 6
d) 8
Answer: b) 7. 1 Crore = 1,00,00,000 (seven zeros).
2. 1 Lakh = ___ Thousands
a) 10
b) 1,000
c) 100
d) 10,000
Answer: c) 100. 1 Lakh = 1,00,000 = 100 x 1,000.
3. 10 Lakh is equal to:
a) 1 Billion
b) 1 Million
c) 10 Million
d) 100 Thousand
Answer: b) 1 Million. 10,00,000 = 1,000,000.
4. In the Indian system, commas are placed after every ___ digits from the right (after the first three).
a) 2
b) 3
c) 4
d) 1
Answer: a) 2. Indian system: first comma after 3 digits, then every 2 digits.
3. In the International system, commas are placed after every 2 digits.
FALSE. International system uses commas every 3 digits from the right.
4. The population of India is an approximate value, not an exact value.
TRUE. Population changes every second (births, deaths), so we use approximate values.
5. 105 has 5 zeros after the 1.
TRUE. 10^5 = 1,00,000 (1 followed by 5 zeros).
6. 7,456 rounded to nearest 100 is 7,500.
TRUE. Tens digit is 5 (>= 5), so we round up from 7,400 to 7,500.
7. The nearest star to Earth (after Sun) is about 40 lakh crore km away.
TRUE. Proxima Centauri is ~4.24 light years away = ~40 lakh crore km.
8. Your heart beats about 1 lakh times per day.
TRUE (approximately). 72 x 60 x 24 = 1,03,680 ~ just over 1 lakh.
9. 100 Crore = 1 Billion
TRUE. 100 x 1,00,00,000 = 1,00,00,00,000 = 1,000,000,000.
10. A lakh has 6 zeros.
FALSE. 1 Lakh = 1,00,000 has only 5 zeros.
11. 3 x 104 = 3,00,000
FALSE. 3 x 10^4 = 3 x 10,000 = 30,000 (not 3,00,000).
12. The number of students in your class is an approximate value.
FALSE. This is an exact value - you can count every student precisely.
13. Goa is the smallest Indian state by population with about 15 lakh people.
TRUE. Goa has approximately 15,00,000 people, the smallest state population.
14. 87,654 rounded to the nearest ten thousand is 90,000.
TRUE. Thousands digit is 7 (>= 5), round up from 80,000 to 90,000.
15. Light from the Sun takes about 8 minutes to reach Earth.
TRUE. More precisely, about 8 minutes 20 seconds.
📖 Long Answer Questions (10 Questions)
1. Explain the Indian place value system. How does it differ from the International system?
The Indian Place Value System groups digits as: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores, and so on. Commas are placed after the first 3 digits from the right, then every 2 digits (pattern: 3-2-2-2...).
The International System groups digits as: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, etc. Commas are placed every 3 digits from the right (pattern: 3-3-3-3...).
Key differences: The Indian system uses Lakh (1,00,000) and Crore (1,00,00,000), while the International system uses Million (1,000,000) and Billion (1,000,000,000). 1 Million = 10 Lakh, and 1 Billion = 100 Crore.
2. What are powers of 10? Explain the pattern with examples from 101 to 107.
Powers of 10 represent repeated multiplication of 10 by itself.
Pattern: The exponent (power) tells the number of zeros. To multiply any number by a power of 10, just add that many zeros to the number. E.g., 5 x 103 = 5,000.
3. Explain the rules of rounding with examples for rounding to nearest 10, 100, 1000, and lakh.
Rounding Rule: Look at the digit immediately to the right of the place you're rounding to. If it's 5 or more, round up. If it's less than 5, round down.
Nearest 10: 67 rounds to 70 (7 >= 5), 23 rounds to 20 (3 < 5) Nearest 100: 2,567 rounds to 2,600 (6 >= 5), 823 rounds to 800 (2 < 5) Nearest 1,000: 7,891 rounds to 8,000 (8 >= 5), 4,325 rounds to 4,000 (3 < 5) Nearest Lakh: 3,65,000 rounds to 4,00,000 (6 >= 5), 3,45,000 rounds to 3,00,000 (4 < 5)
Memory: "5 or more, raise the score. 4 or less, let it rest!"
4. How do you convert between Indian and International number systems? Give 3 examples.
The number value stays the same - only the way we group and name digits changes.
Example 1: 25,00,000 (Indian: Twenty-five lakh) = 2,500,000 (International: Two million five hundred thousand) Example 2: 3,50,00,000 (Indian: Three crore fifty lakh) = 35,000,000 (International: Thirty-five million) Example 3: 1,20,00,00,000 (Indian: One hundred twenty crore) = 1,200,000,000 (International: One billion two hundred million)
5. Write 5 real-world examples each of exact values and approximate values. Why is this distinction important?
Exact values: (1) Score in an exam - 87/100, (2) Students in class - 42, (3) Money in wallet - Rs 450, (4) Chapters in textbook - 15, (5) Players in a cricket team - 11.
Approximate values: (1) India's population - ~144 crore, (2) Stars visible at night - ~3,000, (3) Crowd at a concert - ~50,000, (4) Trees in a forest - ~lakhs, (5) Grains of sand on a beach - ~crores.
Why important: For banking, exams, and measurements, we need exact numbers. For very large quantities that change constantly or are hard to count, approximate values are practical and sufficient. Using the wrong type can lead to confusion or errors.
6. Calculate how many times your heart beats in your lifetime (assume 75 years, 72 beats/min). Express in crore.
Beats per minute = 72
Beats per hour = 72 x 60 = 4,320
Beats per day = 4,320 x 24 = 1,03,680
Beats per year = 1,03,680 x 365 = 3,78,43,200
Beats in 75 years = 3,78,43,200 x 75 = 2,83,82,40,000
= approximately 284 crore heartbeats or about 2.84 billion beats!
This is almost 3 arab (billion) beats in a lifetime - all happening automatically without us even thinking about it!
7. If light travels at 3,00,000 km/s, how long does it take to reach Earth from the Sun (15 crore km away)?
Distance = 15,00,00,000 km (15 crore km)
Speed of light = 3,00,000 km/s
Time = Distance / Speed = 15,00,00,000 / 3,00,000 = 500 seconds
500 seconds = 8 minutes 20 seconds
So when you see the Sun, you're actually seeing it as it was 8 minutes and 20 seconds ago! If the Sun suddenly went dark, we wouldn't know for over 8 minutes.
8. Compare the populations of Goa (15 lakh) and Uttar Pradesh (24 crore). Express UP's population in terms of Goa's.
Goa = 15,00,000 (15 lakh)
UP = 24,00,00,000 (24 crore)
Ratio = 24,00,00,000 / 15,00,000 = 160
UP's population is 160 times that of Goa! You would need 160 Goas to match UP's population. This shows the incredible diversity in state sizes within India.
9. A school wants to collect Rs 10,00,000 (10 lakh) for charity. If each of 1,250 students collects equal amount, how much should each collect?
Total to collect = Rs 10,00,000
Number of students = 1,250
Amount per student = 10,00,000 / 1,250 = Rs 800
Each student needs to collect Rs 800. If this is done over 4 months, that's Rs 200/month or about Rs 7/day per student - very achievable!
10. Why do we need such large numbers? Give examples from daily life, science, and economics.
Large numbers are essential because the world operates at massive scales:
Daily Life: Population counts (144 crore Indians), railway passengers (2.3 crore/day), mobile users (120 crore+). Science: Distance to Sun (15 crore km), cells in body (37 lakh crore), speed of light (3 lakh km/s), age of Earth (450 crore years). Economics: India's GDP (Rs 272 lakh crore), national budget (Rs 48 lakh crore), currency in circulation (Rs 34 lakh crore). Technology: Internet users worldwide (500 crore+), data generated daily (250 crore GB), WhatsApp messages per day (10,000 crore).
Without large numbers and systems to read them, we couldn't measure, compare, or manage the world around us!
🔥 HOTS (Higher Order Thinking Skills) - 5 Questions
1. A billionaire has Rs 100 crore. If he gives away Rs 1 lakh every day, how many years will it take to give away all his money? Can he give it all away in his lifetime?
Rs 100 crore = 1,00,00,00,000
Rs 1 lakh per day = 1,00,000
Days needed = 1,00,00,00,000 / 1,00,000 = 1,00,000 days
Years = 1,00,000 / 365 = ~274 years!
No, he CANNOT give it all away in his lifetime! Even at Rs 1 lakh per day, it would take 274 years. This shows just how massive 100 crore really is.
2. If you stack 1 crore one-rupee coins (thickness: 1.5 mm each), how tall would the stack be? Compare with Mt. Everest (8,849 m).
1 crore coins = 1,00,00,000 coins
Thickness per coin = 1.5 mm
Total height = 1,00,00,000 x 1.5 mm = 1,50,00,000 mm
= 15,000 m = 15 km!
Mt. Everest = 8.849 km
The stack would be 15/8.849 = ~1.7 times taller than Mt. Everest!
It would even be higher than where commercial planes fly (~10-12 km)!
3. India's population grows by about 1 crore per year. At this rate, estimate India's population in the year 2050. What challenges might this create?
Current population (2024) = ~144 crore
Growth rate = ~1 crore/year
Years to 2050 = 26 years
Additional population = 26 crore
Estimated 2050 population = 144 + 26 = ~170 crore
Challenges: More food needed (we need to grow 18% more food), more houses, more schools and hospitals, more jobs, more water (India already faces water stress), more energy, and greater strain on natural resources. This is why population awareness and sustainable development are crucial!
4. Why can't we express the exact number of grains of sand on a beach or stars in the sky? What does this tell us about the difference between mathematics and the real world?
We can't count them exactly because:
(1) The numbers are astronomically large (estimated 7.5 x 1018 grains of sand on Earth)
(2) They keep changing (waves move sand, stars are born and die)
(3) We can't access all of them (ocean floor sand, distant galaxies)
(4) Counting each one would take longer than a human lifetime
What this tells us: Mathematics gives us perfect, exact tools - we CAN write any number, no matter how large. But the real world is messy and constantly changing. This is why estimation and approximation are just as important as exact counting. Scientists use mathematical models and sampling to estimate these quantities. The beauty of math is that it can handle numbers bigger than anything in the physical universe!
5. A number N when rounded to the nearest lakh gives 7,00,000. What is the smallest and largest possible value of N?
For a number to round to 7,00,000 (nearest lakh):
Smallest value: The number must be at least 6,50,000 (because 6,49,999 would round down to 6,00,000). So smallest N = 6,50,000.
Largest value: The number must be less than 7,50,000 (because 7,50,000 would round up to 8,00,000). So largest N = 7,49,999.
Range: 6,50,000 ≤ N ≤ 7,49,999
That's a range of exactly 1,00,000 (1 lakh) possible values!
📜Chapter Test Paper
CHAPTER 1 — LARGE NUMBERS AROUND US
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test
Total Marks: 40Time: 1½ Hours
General Instructions:
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Write the numeral for: Thirty-two lakh seven thousand ninety
Q2.1
How many lakhs make one crore?
Q3.1
Round 48,73,562 to the nearest lakh.
Q4.1
Place the correct symbol (<, > or =): 50 lakhs ___ 5 million
Q5.1
A calculator has only a +100 button. How many presses to show 7,200 on the screen?
Q6.1
The product of a 3-digit number and a 2-digit number will have at least ___ digits and at most ___ digits.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Write the following number in both Indian and International systems. Also write in words in both systems. 59,40,38,072
Q8.2
A calculator has buttons: +1, +10, +100, +1000. What is the minimum number of button clicks to reach 47,253? Explain your reasoning.
Q9.2
Find all 4 nearest neighbours of the number 6,83,47,215:
(a) Nearest Thousand (b) Nearest Ten Thousand (c) Nearest Lakh (d) Nearest Crore
Q10.2
Calculate using a shortcut (show the trick):
(a) 248 × 25 (b) 64 × 125
Q11.2
India has approximately 1,00,000 varieties of rice. If a person tastes 4 varieties every day, how many years will it take to taste all of them? (Take 1 year = 365 days)
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Study the table and answer the questions below:
City
Population (2011)
Bengaluru
84,25,970
Hyderabad
68,09,970
Pune
31,15,431
Surat
44,67,797
(a) Arrange the cities in descending order of population.
(b) What is the difference between the populations of Bengaluru and Pune?
(c) Round Hyderabad’s population to the nearest ten lakh.
Q13.3
A school raises funds for flood relief. They collect ₹275 from each of 1,850 students. The principal adds ₹48,500 from the school fund.
(a) What is the total amount collected?
(b) Express the total in words (Indian system).
(c) If the target was ₹6,00,000, how much more is needed?
Q14.3
Estimate the product 489 × 7,210 by rounding each number. Then find the exact product. How close was your estimate?
Q15.3
Using the digits 0, 3, 5, 7, 8 (each used exactly once):
(a) Write the largest 5-digit number.
(b) Write the smallest 5-digit number.
(c) Find the difference between them.
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
(a) A factory produces 12,500 bottles per day. It operates 6 days a week.
(i) How many bottles in a week?
(ii) How many bottles in a year (52 weeks)?
(iii) Express the yearly production in words (Indian system).
(iv) If each bottle weighs 250 grams, what is the total weight in tonnes? (1 tonne = 10,00,000 g)
(b) The factory wants to reach a target of 50 lakh bottles per year. How many extra bottles must they produce daily (over 6 days/week, 52 weeks)?
Q17.5
(a) A satellite orbits the Earth at 28,000 km/hour.
(i) How many km does it travel in one day?
(ii) How many days to cover a distance equal to Earth–Sun (15,00,00,000 km)?
(iii) Round your answer to the nearest hundred days.
(b) The Moon is 3,84,400 km from Earth. If a spacecraft travels at 1,200 km/hour:
(i) How many hours to reach the Moon?
(ii) How many complete days is that? Express the remaining hours too.
Bonus Question (Optional) [2 Marks]
Q18.2
★ A number when rounded to the nearest lakh gives 35,00,000 and when rounded to the nearest ten thousand gives 34,90,000. Find the range of possible values of the number.
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1 Crore = 1,00,00,000
1 Lakh = 1,00,000
1,00,00,000 ÷ 1,00,000 = 100 lakhs make one crore.
Q3. [1 Mark]
48,73,562 → Look at the ten-thousands digit: 7
Since 7 ≥ 5, round up the lakh digit (8 becomes 9).
Wait — let’s be careful: 48,73,562. The lakhs digit is 8. The digit after lakhs place (ten-thousands) is 7.
Since 7 ≥ 5, round up: 48 lakhs becomes 49 lakhs. Answer: 49,00,000
Q4. [1 Mark]
50 lakhs = 50,00,000
5 million = 50,00,000 (since 1 million = 10 lakh)
50,00,000 = 50,00,000 Answer: 50 lakhs = 5 million
Q5. [1 Mark]
7,200 ÷ 100 = 72 presses
Q6. [1 Mark]
Smallest: 100 × 10 = 1,000 (4 digits)
Largest: 999 × 99 = 98,901 (5 digits) Answer: at least 4 digits and at most 5 digits.
Rule: m + n − 1 to m + n digits → 3 + 2 − 1 = 4 to 3 + 2 = 5.
Q7. [2 Marks]
Indian system: 59,40,38,072
In words: Fifty-nine crore forty lakh thirty-eight thousand seventy-two
International system: 594,038,072
In words: Five hundred ninety-four million thirty-eight thousand seventy-two
(1 mark for correct comma placement + 1 mark for correct words in both systems)
Comparison: [1 mark]
Difference = 35,25,690 − 35,00,000 = 25,690
Error percentage = 25,690 / 35,25,690 × 100 ≈ 0.73%
The estimate was very close — less than 1% error!
Q15. [3 Marks]
Available digits: 0, 3, 5, 7, 8
(a) Largest 5-digit number: [1 mark]
Arrange in descending order: 87,530
(b) Smallest 5-digit number: [1 mark]
First digit cannot be 0, so use 3 (smallest non-zero).
Then arrange remaining (0, 5, 7, 8) in ascending: 0, 5, 7, 8 Answer: 30,578
(b) Extra bottles needed daily: [1½ marks]
Target: 50,00,000 bottles/year
Current: 39,00,000 bottles/year
Shortfall: 50,00,000 − 39,00,000 = 11,00,000 bottles/year
Working days/year: 6 × 52 = 312 days
Extra per day: 11,00,000 ÷ 312 ≈ 3,526 extra bottles/day
New daily production ≈ 12,500 + 3,526 = 16,026 bottles/day
Q17. [5 Marks]
(a)(i) Distance in one day: [1 mark]
28,000 × 24 = 6,72,000 km/day
(a)(ii) Days to reach the Sun: [1 mark]
15,00,00,000 ÷ 6,72,000 ≈ 223.2 days
(a)(iii) Rounded to nearest hundred: [½ mark]
223.2 → 200 days (nearest hundred)
(b)(i) Hours to reach the Moon: [1½ marks]
3,84,400 ÷ 1,200 = 320.33 hours
(b)(ii) Complete days + remaining hours: [1 mark]
320.33 ÷ 24 = 13 days remainder 8.33 hours Answer: 13 complete days and approximately 8 hours
Q18. Bonus [2 Marks]
Condition 1: Rounded to nearest lakh = 35,00,000 [1 mark]
This means: 34,50,000 ≤ N ≤ 35,49,999
Condition 2: Rounded to nearest ten thousand = 34,90,000 [1 mark]
This means: 34,85,000 ≤ N ≤ 34,94,999
Both conditions together:
The number must satisfy BOTH ranges.
Intersection: max(34,50,000, 34,85,000) ≤ N ≤ min(35,49,999, 34,94,999)
→ 34,85,000 ≤ N ≤ 34,94,999
The number lies between 34,85,000 and 34,94,999 (a range of 10,000 values).