Class 7 Mathematics Practice Sheet: CBSE Class 7 Mathematics A Peek Beyond the Point Practice Paper Worksheet Set 03 with Answers
Access comprehensive chapter-wise worksheets for Chapter 03 A Peek Beyond the Point using the CBSE Class 7 Mathematics A Peek Beyond the Point Practice Paper Worksheet Set 03 with Answers. Designed to align with the 2026-27 academic syllabus for Class 7 Mathematics, these printable practice sets help students reinforce key concepts and improve their overall exam readiness.
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Practice Paper 09 for Class 7 Maths Ganita Prakash Chapter 3 A Peek Beyond the Point carries 40 marks across 20 questions in Sections A to E, and the answers below explain every step. This paper works with decimals written as tenths and hundredths (like 5 and 8 tenths), place value and expanded form, reading decimal numbers aloud, writing rupees and paise or metres and centimetres as decimals, and word problems on cutting wood and fabric, a car's journey, a honeybee's body length and rods for toy cars.
Section A: Multiple Choice Questions (1 Mark Each)
(a) 1 cm and 1 one-tenth
(b) 1 cm and 1 hundredth
(c) 11 cm
(d) 10 cm
Show Answer & Explanation
Answer: (a) 1 cm and 1 one-tenth
Explanation:
1. Total = \( \frac{4}{10} \) + \( \frac{7}{10} \) = \( \frac{11}{10} \) cm.
2. \( \frac{11}{10} \) = \( \frac{10}{10} \) + \( \frac{1}{10} \) = 1 + \( \frac{1}{10} \) cm.
3. So the snail covers 1 cm and 1 one-tenth (1.1 cm).
Teacher's Note:
1. Ten tenths make one whole, so 11 tenths = 1 whole and 1 tenth.
2. 11 cm would be 11 wholes, not 11 tenths.
(a) 350
(b) 35
(c) 305
(d) 3050
Show Answer & Explanation
Answer: (a) 350
Explanation:
1. 1 unit = 10 tenths = 100 hundredths, so 3 units = 300 hundredths.
2. 1 tenth = 10 hundredths, so 5 tenths = 50 hundredths.
3. Total = 300 + 50 = 350 one-hundredths (3.5 = 3.50 = 350 hundredths).
Teacher's Note:
1. Change everything into the smallest unit asked for, then add.
2. 35 is the number of tenths, not hundredths.
(a) 16.1 cm
(b) 10.0 cm
(c) 9.0 cm
(d) 16.9 cm
Show Answer & Explanation
Answer: (b) 10.0 cm
Explanation:
1. Length of the first two pieces = 7.1 + 8.8 = 15.9 cm.
2. Third piece = 25.9 − 15.9 = 10.0 cm.
Teacher's Note:
1. Add the known pieces first, then subtract from the whole.
2. Check: 7.1 + 8.8 + 10.0 = 25.9.
(a) 3.4
(b) 0.34
(c) 34.0
(d) 0.034
Show Answer & Explanation
Answer: (b) 0.34
Explanation:
1. 34 hundredths = \( \frac{34}{100} \).
2. This is 3 tenths and 4 hundredths, written as 0.34.
Teacher's Note:
1. Hundredths need two places after the point.
2. 3.4 is 34 tenths and 0.034 is 34 thousandths.
(a) 40
(b) 4
(c) \( \frac{4}{10} \)
(d) \( \frac{4}{100} \)
Show Answer & Explanation
Answer: (c) \( \frac{4}{10} \)
Explanation:
1. In 20.47, the digit just after the decimal point is in the tenths place.
2. The digit 4 is in the tenths place, so its place value is 4 × \( \frac{1}{10} \) = \( \frac{4}{10} \) (0.4).
Teacher's Note:
1. Place value = digit × value of its place.
2. The 7 in 20.47 has place value 7/100.
(a) 156 mm
(b) 15.6 mm
(c) 1.56 mm
(d) 0.156 mm
Show Answer & Explanation
Answer: (a) 156 mm
Explanation:
1. 1 cm = 10 mm.
2. 15.6 cm = 15.6 × 10 mm = 156 mm.
Teacher's Note:
1. Going to a smaller unit gives a bigger number.
2. Multiplying by 10 moves the decimal point one place right.
(a) 0.09 cm
(b) 0.8 cm
(c) 1.0 cm
(d) 0.01 cm
Show Answer & Explanation
Answer: (a) 0.09 cm
Explanation:
1. 1 mm = 0.1 cm, so 0.8 mm = 0.08 cm and 1 mm = 0.1 cm.
2. The ant's length must lie between 0.08 cm and 0.10 cm.
3. 0.09 cm = 0.9 mm lies between them, so the answer is 0.09 cm.
4. 0.8 cm = 8 mm and 1.0 cm = 10 mm are far too long; 0.01 cm = 0.1 mm is far too short.
Teacher's Note:
1. Change the given range into the unit of the options first.
2. Divide mm by 10 to get cm.
(a) 2.07 m
(b) 2.7 m
(c) 2.007 m
(d) 2.70 m
Show Answer & Explanation
Answer: (a) 2.07 m
Explanation:
1. 1 cm = \( \frac{1}{100} \) m = 0.01 m, so 7 cm = 0.07 m.
2. 2 m 7 cm = 2 + 0.07 = 2.07 m.
Teacher's Note:
1. Centimetres are hundredths of a metre, so they take two decimal places.
2. 2.7 m would be 2 m 70 cm.
Assertion (A): The number 15.06 is read as "fifteen point zero six".
Reason (R): In decimal notation, the digits after the decimal point are read as individual digits, not as a single number. For example, 0.274 is read as "zero point two seven four".
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. After the point in 15.06, the digits are 0 and 6, read one by one: “fifteen point zero six”. The Assertion is true.
2. The Reason states the rule for reading digits after the point, and the example is read correctly. The Reason is true.
3. The Assertion follows from this rule, so the answer is (a).
Teacher's Note:
1. Never read 15.06 as “fifteen point six”; the zero must be said.
2. 15.06 can also be read as fifteen and six hundredths.
Assertion (A): 10 rupees and 5 paise can be written as 10.05 rupees.
Reason (R): 1 paisa is equal to \( \frac{1}{100} \) of a rupee, so 5 paise is equal to \( \frac{5}{100} \) of a rupee or 0.05 rupees.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. 5 paise = 5 hundredths of a rupee = ₹0.05, so the Reason is true.
2. ₹10 and 5 paise = 10 + 0.05 = ₹10.05, so the Assertion is true.
3. The Assertion is obtained directly from the Reason, so the answer is (a).
Teacher's Note:
1. Paise always take two decimal places: 5 paise is .05, not .5.
2. ₹10.5 would mean 10 rupees 50 paise.
Section B: Short Answer Questions (2 Marks Each)
Question 11. What is the difference in length between a hummingbird egg (1.3 cm long) and the Philippine Goby fish (0.9 cm long)?
Answer:
Hummingbird egg = 1.3 cm and Philippine Goby = 0.9 cm.
1.3 cm = 13 tenths and 0.9 cm = 9 tenths; 13 − 9 = 4 tenths.
Difference = 1.3 − 0.9 = 0.4 cm.
In simple words: The egg is 0.4 cm (4 mm) longer than the fish.
Teacher's Note:
1. Counting in tenths makes the subtraction a simple whole-number one.
2. We cannot take 9 tenths from 3 tenths, so borrow 1 one = 10 tenths.
Question 12. Convert the following:
(a) 15 cm into meters.
(b) 750 g into kilograms.
Answer:
(a) 1 m = 100 cm, so 15 cm = \( \frac{15}{100} \) m = 0.15 m.
(b) 1 kg = 1000 g, so 750 g = \( \frac{750}{1000} \) kg = 0.750 kg = 0.75 kg.
In simple words: Divide cm by 100 for metres and g by 1000 for kilograms.
Teacher's Note:
1. The number of zeros in 100 or 1000 tells how many places the point moves left.
2. 750 g is three-quarters of a kilogram.
Answer:
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 1 | 5 | . | 3 | 4 |
Expanded form: 15.34 = 1 × 10 + 5 × 1 + 3 × \( \frac{1}{10} \) + 4 × \( \frac{1}{100} \)
= 10 + 5 + 0.3 + 0.04.
In words: fifteen point three four (or fifteen and thirty-four hundredths).
In simple words: 15.34 is 1 ten, 5 ones, 3 tenths and 4 hundredths.
Teacher's Note:
1. Each digit is multiplied by the value of its place.
2. Read the digits after the point one by one: “point three four”, not “point thirty-four”.
Question 14. A small sheet of paper is \( 5\frac{8}{10} \) units long. If it is folded in half, what is its new length?
Answer:
\( 5\frac{8}{10} \) units = 5.8 units.
Folding in half halves the length: 5.8 ÷ 2.
5 ÷ 2 = 2.5 and 0.8 ÷ 2 = 0.4, so 5.8 ÷ 2 = 2.5 + 0.4 = 2.9.
New length = 2.9 units (\( 2\frac{9}{10} \) units).
In simple words: Half of 5.8 is 2.9, so the folded paper is 2.9 units long.
Teacher's Note:
1. Think of 5.8 as 58 tenths; half of 58 tenths is 29 tenths = 2.9.
2. Check: 2.9 + 2.9 = 5.8.
Section C: Short Answer Questions (3 Marks Each)
Answer:
Total length cut = 1.50 + 2.75 + 0.80:
| 1.50 |
| + 2.75 |
| + 0.80 |
| 5.05 |
Wood left = 6.00 − 5.05 = 0.95 m (95 cm).
In simple words: The three pieces use 5.05 m, leaving 0.95 m of the 6 m plank.
Teacher's Note:
1. Write 1.5 as 1.50, 0.8 as 0.80 and 6 as 6.00 before working.
2. Check: 5.05 + 0.95 = 6.00.
Question 16. Find the sum and difference of the following two lengths: 12 units and 4 one-tenths, and 6 units and 7 one-tenths.
Answer:
First length = 12 units and 4 tenths = 12.4 units; second length = 6 units and 7 tenths = 6.7 units.
Sum: (12 + 6) units + (4 + 7) tenths = 18 units + 11 tenths.
11 tenths = 1 unit + 1 tenth, so the sum = 19 units and 1 tenth = 19.1 units (\( 19\frac{1}{10} \)).
Difference: 4 tenths − 7 tenths is not possible, so borrow 1 unit = 10 tenths: 12 units 4 tenths = 11 units 14 tenths.
(11 − 6) units + (14 − 7) tenths = 5 units and 7 tenths = 5.7 units (\( 5\frac{7}{10} \)).
In simple words: 12.4 + 6.7 = 19.1 units and 12.4 − 6.7 = 5.7 units.
Teacher's Note:
1. Ten tenths make one unit, so carry or borrow across the point just like with whole numbers.
2. Check: 5.7 + 6.7 = 12.4.
Question 17. A car travels at a constant speed. In 1 hour, it covers \( 65\frac{4}{10} \) km. In the next hour, it covers \( 68\frac{9}{10} \) km. What is the total distance covered by the car in two hours?
Answer:
First hour = \( 65\frac{4}{10} \) km = 65.4 km; second hour = \( 68\frac{9}{10} \) km = 68.9 km.
Total = 65.4 + 68.9: tenths 4 + 9 = 13 tenths = 1 unit 3 tenths; units 65 + 68 + 1 = 134.
Total distance = 134.3 km.
In simple words: 65.4 km + 68.9 km = 134.3 km in two hours.
Teacher's Note:
1. Changing mixed numbers with tenths into decimals makes adding easy.
2. The question calls the speed constant, but the two distances differ; just add what was covered.
Section D: Long Answer Question (5 Marks)
(a) If he uses 12 meters and 75 centimeters for a dress, what is the remaining length of the fabric?
(b) The tailor then decides to make 8 similar scarves, each requiring 1.25 meters of fabric. What is the total length of fabric required for the scarves, and how much fabric is left after making the scarves?
Answer:
(a) 75 cm = 0.75 m, so the dress uses 12 m 75 cm = 12.75 m.
| 45.80 |
| − 12.75 |
| 33.05 |
Fabric remaining = 33.05 m.
(b) Fabric for 8 scarves = 8 × 1.25 m = 10.00 m (since 4 × 1.25 = 5, double it is 10).
Total fabric required for the scarves = 10 m.
Fabric left = 33.05 − 10.00 = 23.05 m.
In simple words: After the dress 33.05 m is left; the scarves take 10 m, leaving 23.05 m.
Teacher's Note:
1. Change 12 m 75 cm into 12.75 m before subtracting.
2. 1.25 × 8: 1 × 8 = 8 and 0.25 × 8 = 2, so the product is 10.
3. Check: 12.75 + 10 + 23.05 = 45.8 m.
Section E: Case Study Based Questions (4 Marks Each)
Question 19. Case Study 1: The Bee's Journey
A honeybee, in search of nectar, flies a total distance equivalent to the length of its body parts. The length of its head is \( 2\frac{3}{10} \) units, its thorax is \( 5\frac{4}{10} \) units, and its abdomen is \( 7\frac{5}{10} \) units. On its return journey, it carries pollen, which increases its total length by \( 1\frac{1}{10} \) units.
Based on this information, answer the following questions:
(a) What is the total length of the honeybee's body? (2 marks)
(b) What is the total length of the bee when it is carrying pollen? (2 marks)
Answer:
Head = \( 2\frac{3}{10} \) = 2.3 units, thorax = \( 5\frac{4}{10} \) = 5.4 units, abdomen = \( 7\frac{5}{10} \) = 7.5 units.
(a) Units: 2 + 5 + 7 = 14; tenths: 3 + 4 + 5 = 12 tenths = 1 unit and 2 tenths.
Total body length = 14 + 1.2 = 15.2 units.
(b) With pollen: 15.2 + \( 1\frac{1}{10} \) = 15.2 + 1.1 = 16.3 units.
In simple words: The bee's body is 15.2 units long, and 16.3 units with pollen.
Teacher's Note:
1. Add the whole parts and the tenths separately, then regroup 10 tenths into 1 unit.
2. Writing each mixed number as a decimal first gives the same result.
Question 20. Case Study 2: The Toy Factory
A toy factory manufactures miniature cars. Each car requires a metal rod of length 18.5 cm. The factory buys large rods that are 10 meters long.
(a) How many miniature cars can be made from a single 10 meter long rod? (2 marks)
(b) After cutting the required pieces for the cars, what is the length of the leftover rod? (2 marks)
Answer:
(a) Change to the same unit: 10 m = 10 × 100 = 1000 cm.
Try multiples of 18.5: 18.5 × 50 = 925 cm, 18.5 × 54 = 999 cm, 18.5 × 55 = 1017.5 cm (too long).
So 54 miniature cars can be made from one rod.
(b) Length used = 54 × 18.5 = 999 cm.
Leftover rod = 1000 − 999 = 1 cm.
In simple words: 54 pieces of 18.5 cm use 999 cm of the 1000 cm rod, leaving 1 cm.
Teacher's Note:
1. Only whole cars count, so take the largest number of pieces that fits.
2. 18.5 × 54 = 18.5 × 50 + 18.5 × 4 = 925 + 74 = 999.
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