💡 Print paper or share solutions as PDF.
CHAPTER 3 — A PEEK BEYOND THE POINT
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test — Set 1 (Foundation)
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.
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 9/10 as a decimal number.
Q2.1
In the decimal 6.83, which digit is in the hundredths place?
Q3.1
Which is greater: 0.5 or 0.50? Justify your answer.
Q4.1
Add: 3.4 + 2.5
Q5.1
Write 0.75 as a fraction in its simplest form.
Q6.1
Write in decimal form: “Forty-five hundredths.”
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Convert 2/5 to a decimal. Show your steps clearly.
Q8.2
Arrange in ascending order: 3.2, 3.02, 3.20, 3.21
Show your comparison step by step.
Show your comparison step by step.
Q9.2
Subtract: 8.75 − 4.30
Show working by aligning decimal points.
Show working by aligning decimal points.
Q10.2
Riya buys items costing ₹18.50 and ₹24.75. She pays ₹50. How much change does she get? Show all steps.
Q11.2
Multiply: (a) 5.3 × 10 (b) 5.3 × 100
State the rule used.
State the rule used.
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Write the place value of each digit in 47.365. Present your answer as a table with columns: Digit | Place | Place Value.
Q13.3
(a) Write 67.04 in expanded form.
(b) Write the decimal from its expanded form: 50 + 3 + 7/10 + 2/100
(c) How many times is 0.7 greater than 0.07?
(b) Write the decimal from its expanded form: 50 + 3 + 7/10 + 2/100
(c) How many times is 0.7 greater than 0.07?
Q14.3
A tailor has a cloth of length 12.5 m. She uses 3.75 m for a shirt and 4.25 m for trousers.
(a) Write a single expression for cloth remaining.
(b) Find the answer.
(c) If she needs one more shirt (3.75 m), does she have enough cloth? Justify.
(a) Write a single expression for cloth remaining.
(b) Find the answer.
(c) If she needs one more shirt (3.75 m), does she have enough cloth? Justify.
Q15.3
The lengths of three sticks are 2.35 m, 1.8 m and 0.95 m.
(a) Find the total length.
(b) Find the difference between the longest and the shortest stick.
(c) If they are placed end to end, will they reach a wall 5 m away? By how much do they fall short or exceed?
(a) Find the total length.
(b) Find the difference between the longest and the shortest stick.
(c) If they are placed end to end, will they reach a wall 5 m away? By how much do they fall short or exceed?
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
A shopkeeper buys the following items:
(a) Find the cost of rice. [1]
(b) Find the cost of sugar. [1]
(c) Find the cost of oil. [1]
(d) Find the total amount spent. [1]
(e) She pays ₹400. Find the balance returned. [1]
| Item | Quantity | Rate |
|---|---|---|
| Rice | 2.5 kg | ₹40 per kg |
| Sugar | 1.75 kg | ₹48 per kg |
| Oil | 0.5 litre | ₹120 per litre |
(b) Find the cost of sugar. [1]
(c) Find the cost of oil. [1]
(d) Find the total amount spent. [1]
(e) She pays ₹400. Find the balance returned. [1]
Q17.5
(a) Put these decimals in descending order: 4.5, 4.05, 4.55, 4.505. Show your comparison step by step. [2]
(b) Find the sum of the largest and smallest number from part (a). [1]
(c) Find the difference between the largest and smallest from part (a). [1]
(d) Multiply the smallest value from part (a) by 100. [1]
(b) Find the sum of the largest and smallest number from part (a). [1]
(c) Find the difference between the largest and smallest from part (a). [1]
(d) Multiply the smallest value from part (a) by 100. [1]
Bonus Question (Optional) [2 Marks]
Q18.2
★ A decimal number has 2 decimal places. Its whole part is 7. The digit in the tenths place is 3 more than the digit in the hundredths place. The sum of all three digits (whole, tenths, hundredths) is 12. Find the decimal number.
Preeti Kushwah Classes
Scan for more notes & papers
www.preetikushwahclasses.com
Scan for more notes & papers
www.preetikushwahclasses.com
Answer Key & Detailed Solutions
Q1. [1 Mark]
9/10 = 0.9
(Denominator is 10 → 1 decimal place)
(Denominator is 10 → 1 decimal place)
Q2. [1 Mark]
6.83: tenths place = 8, hundredths place = 3
Answer: 3
Answer: 3
Q3. [1 Mark]
They are equal. 0.5 = 0.50
A trailing zero after the last non-zero digit in the decimal part does not change the value.
Neither is greater — 0.5 = 0.50.
A trailing zero after the last non-zero digit in the decimal part does not change the value.
Neither is greater — 0.5 = 0.50.
Q4. [1 Mark]
3.4 + 2.5 = 5.9
Q5. [1 Mark]
0.75 = 75/100
HCF of 75 and 100 = 25
75/100 = 3/4
HCF of 75 and 100 = 25
75/100 = 3/4
Q6. [1 Mark]
“Forty-five hundredths” = 45/100 = 0.45
Q7. [2 Marks]
2/5 — we need denominator = 10.
Multiply numerator and denominator by 2:
2/5 = (2×2)/(5×2) = 4/10 = 0.4
Multiply numerator and denominator by 2:
2/5 = (2×2)/(5×2) = 4/10 = 0.4
Q8. [2 Marks]
Convert to like decimals (2 decimal places): 3.20, 3.02, 3.20, 3.21
Compare hundredths: 3.02 (02) < 3.20 (20) = 3.20 (20) < 3.21 (21)
Ascending order: 3.02 < 3.2 = 3.20 < 3.21
Compare hundredths: 3.02 (02) < 3.20 (20) = 3.20 (20) < 3.21 (21)
Ascending order: 3.02 < 3.2 = 3.20 < 3.21
Q9. [2 Marks]
8.75
− 4.30
――――
= 4.45
− 4.30
――――
= 4.45
Q10. [2 Marks]
Total spent = ₹18.50 + ₹24.75 = ₹43.25
Change = ₹50.00 − ₹43.25 = ₹6.75
Change = ₹50.00 − ₹43.25 = ₹6.75
Q11. [2 Marks]
(a) 5.3 × 10 = 53 (shift decimal 1 place right)
(b) 5.3 × 100 = 530 (shift decimal 2 places right)
Rule: Multiplying a decimal by 10 shifts the decimal point one place to the right. By 100 shifts it two places right.
(b) 5.3 × 100 = 530 (shift decimal 2 places right)
Rule: Multiplying a decimal by 10 shifts the decimal point one place to the right. By 100 shifts it two places right.
Q12. [3 Marks]
47.365 — Place value table:
| Digit | Place | Place Value |
|---|---|---|
| 4 | Tens | 40 |
| 7 | Ones | 7 |
| 3 | Tenths | 0.3 |
| 6 | Hundredths | 0.06 |
| 5 | Thousandths | 0.005 |
Q13. [3 Marks]
(a) 67.04 = 60 + 7 + 0.04 (or: 60 + 7 + 4/100)
(b) 50 + 3 + 7/10 + 2/100 = 53 + 0.7 + 0.02 = 53.72
(c) 0.7 ÷ 0.07 = 7/10 ÷ 7/100 = 7/10 × 100/7 = 10
So 0.7 is 10 times greater than 0.07.
(b) 50 + 3 + 7/10 + 2/100 = 53 + 0.7 + 0.02 = 53.72
(c) 0.7 ÷ 0.07 = 7/10 ÷ 7/100 = 7/10 × 100/7 = 10
So 0.7 is 10 times greater than 0.07.
Q14. [3 Marks]
(a) Expression: 12.5 − 3.75 − 4.25
(b) 12.50 − 3.75 = 8.75; 8.75 − 4.25 = 4.50 m
(c) Cloth remaining = 4.50 m; cloth needed for another shirt = 3.75 m
4.50 ≥ 3.75, so Yes, she has enough cloth. She will have 4.50 − 3.75 = 0.75 m left over.
(b) 12.50 − 3.75 = 8.75; 8.75 − 4.25 = 4.50 m
(c) Cloth remaining = 4.50 m; cloth needed for another shirt = 3.75 m
4.50 ≥ 3.75, so Yes, she has enough cloth. She will have 4.50 − 3.75 = 0.75 m left over.
Q15. [3 Marks]
(a) 2.35 + 1.80 + 0.95 = 2.35 + 1.80 = 4.15; 4.15 + 0.95 = 5.10 m
(b) Longest = 2.35 m, Shortest = 0.95 m
2.35 − 0.95 = 1.40 m
(c) Total length = 5.10 m > 5 m, so Yes, they will reach the wall.
They exceed by 5.10 − 5.00 = 0.10 m.
(b) Longest = 2.35 m, Shortest = 0.95 m
2.35 − 0.95 = 1.40 m
(c) Total length = 5.10 m > 5 m, so Yes, they will reach the wall.
They exceed by 5.10 − 5.00 = 0.10 m.
Q16. [5 Marks]
(a) Rice: 2.5 × 40 = ₹100.00
(b) Sugar: 1.75 × 48 = 1.75 × 48 = (1 × 48) + (0.75 × 48) = 48 + 36 = ₹84.00
(c) Oil: 0.5 × 120 = ₹60.00
(d) Total = 100 + 84 + 60 = ₹244.00
(e) Balance = 400 − 244 = ₹156.00
(b) Sugar: 1.75 × 48 = 1.75 × 48 = (1 × 48) + (0.75 × 48) = 48 + 36 = ₹84.00
(c) Oil: 0.5 × 120 = ₹60.00
(d) Total = 100 + 84 + 60 = ₹244.00
(e) Balance = 400 − 244 = ₹156.00
Q17. [5 Marks]
(a) Convert to like decimals (3 places): 4.500, 4.050, 4.550, 4.505
Compare: 4.550 > 4.505 > 4.500 > 4.050
Descending: 4.55 > 4.505 > 4.5 > 4.05
(b) Largest = 4.55, Smallest = 4.05
Sum = 4.55 + 4.05 = 8.60
(c) Difference = 4.55 − 4.05 = 0.50
(d) Smallest (4.05) × 100 = 405
Compare: 4.550 > 4.505 > 4.500 > 4.050
Descending: 4.55 > 4.505 > 4.5 > 4.05
(b) Largest = 4.55, Smallest = 4.05
Sum = 4.55 + 4.05 = 8.60
(c) Difference = 4.55 − 4.05 = 0.50
(d) Smallest (4.05) × 100 = 405
Q18. [Bonus — 2 Marks]
Let hundredths digit = d.
Then tenths digit = d + 3.
Whole part = 7.
Sum of digits: 7 + (d + 3) + d = 12
⇒ 10 + 2d = 12 ⇒ 2d = 2 ⇒ d = 1
Tenths digit = 1 + 3 = 4, Hundredths digit = 1
The decimal number is 7.41
Verification: 7 + 4 + 1 = 12 ✓
Then tenths digit = d + 3.
Whole part = 7.
Sum of digits: 7 + (d + 3) + d = 12
⇒ 10 + 2d = 12 ⇒ 2d = 2 ⇒ d = 1
Tenths digit = 1 + 3 = 4, Hundredths digit = 1
The decimal number is 7.41
Verification: 7 + 4 + 1 = 12 ✓