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Class 7 Maths Ganita Prakash Chapter 3 A Peek Beyond the Point Practice Paper 07 is a 40-mark test of 20 questions in Sections A to E, with step-by-step answers for every question. It checks reading decimals in ones, tenths and hundredths, comparing and ordering decimals, converting between mm, cm, m, g, kg, litres and kilolitres, and adding and subtracting decimals in real-life problems on cloth, water tanks, plant roots and wooden planks.
Section A: Multiple Choice Questions (1 Mark Each)
(a) 43 tenths of a meter
(b) 3 tenths and 4 hundredths of a meter
(c) 3 ones and 4 tenths of a meter
(d) 34 hundredths of a meter
Show Answer & Explanation
Answer: (c) 3 ones and 4 tenths of a meter
Explanation:
1. In 3.4, the digit 3 is in the ones place and the digit 4 is in the tenths place.
2. So 3.4 m = 3 m + 4 × \( \frac{1}{10} \) m.
3. This is 3 ones and 4 tenths of a meter.
4. 43 tenths = 4.3 m, 3 tenths and 4 hundredths = 0.34 m and 34 hundredths = 0.34 m, so the other options are wrong.
Teacher's Note:
1. The first digit after the point counts tenths, the second counts hundredths.
2. 3.4 can also be read as 34 tenths, but 43 tenths is 4.3.
(a) \( 1\frac{2}{10} \) and \( \frac{12}{10} \)
(b) 1.20 and 1.2
(c) 0.50 and 0.5
(d) All of the above
Show Answer & Explanation
Answer: (d) All of the above
Explanation:
1. \( 1\frac{2}{10} \) = \( \frac{10}{10} \) + \( \frac{2}{10} \) = \( \frac{12}{10} \), so pair (a) is equal.
2. 1.20 = 1 + 2 tenths + 0 hundredths = 1.2, so pair (b) is equal.
3. 0.50 = 5 tenths + 0 hundredths = 0.5, so pair (c) is equal.
4. Every pair shows the same length, so the answer is All of the above.
Teacher's Note:
1. A zero written at the end of the decimal part does not change the value.
2. A mixed number and its improper fraction are two ways of writing one number.
(a) 0.05 m
(b) 0.5 m
(c) 0.005 m
(d) 0.0005 m
Show Answer & Explanation
Answer: (a) 0.05 m
Explanation:
1. 1 m = 100 cm, so 1 cm = \( \frac{1}{100} \) m = 0.01 m.
2. 5 cm = 5 × 0.01 m = \( \frac{5}{100} \) m.
3. 5 hundredths is written as 0.05 m.
Teacher's Note:
1. To change cm to m, divide by 100: the decimal point moves two places to the left.
2. 0.5 m would be 50 cm, which is ten times too much.
(a) 0.405 < 0.45 < 0.504 < 0.54
(b) 0.405 < 0.45 < 0.54 < 0.504
(c) 0.45 < 0.405 < 0.504 < 0.54
(d) 0.504 < 0.45 < 0.405 < 0.54
Show Answer & Explanation
Answer: (a) 0.405 < 0.45 < 0.504 < 0.54
Explanation:
1. Write all numbers with three decimal places: 0.450, 0.405, 0.540, 0.504.
2. Compare them like whole numbers of thousandths: 405 < 450 < 504 < 540.
3. So the increasing order is 0.405 < 0.45 < 0.504 < 0.54.
Teacher's Note:
1. Padding with zeros makes every number the same length, so comparing becomes easy.
2. A longer decimal is not always bigger: 0.405 is smaller than 0.45.
(a) 4 balls
(b) 3 balls
(c) 22 balls
(d) 20 balls
Show Answer & Explanation
Answer: (c) 22 balls
Explanation:
1. In cricket, 1 over = 6 balls. The scoreboard writes overs as “overs.balls”, so 3.4 means 3 overs and 4 balls (it is not a decimal of 3.4 overs).
2. 3 overs = 3 × 6 = 18 balls.
3. Balls left = 18 + 4 = 22 balls.
Teacher's Note:
1. The digit after the point in cricket overs counts balls, and it never goes beyond 5.
2. This is an example where a point does not mean tenths.
(a) 5.01
(b) 4.95
(c) 4.89
(d) 5.1
Show Answer & Explanation
Answer: (a) 5.01
Explanation:
1. Find the distance of each number from 5.
2. 5.01 − 5 = 0.01; 5 − 4.95 = 0.05; 5 − 4.89 = 0.11; 5.1 − 5 = 0.1.
3. The smallest distance is 0.01, so 5.01 is closest to 5.
Teacher's Note:
1. Closeness is measured by the gap on the number line, whichever side the number is on.
2. Compare the gaps 0.01, 0.05, 0.1 and 0.11 as decimals.
(a) 0.75 kg
(b) 0.80 kg
(c) 0.85 kg
(d) 0.95 kg
Show Answer & Explanation
Answer: (b) 0.80 kg
Explanation:
1. Write each weight with two decimal places: 0.50 + 0.25 + 0.05.
2. Add the hundredths: 50 + 25 + 5 = 80 hundredths.
3. So the total is 0.80 kg (that is 800 g).
Teacher's Note:
1. Line up the decimal points before adding.
2. 0.80 kg and 0.8 kg are the same weight.
(a) 1 mm = 0.001 m
(b) 1 g = 0.001 kg
(c) 1 cm = 0.01 m
(d) 1 mm = 0.01 cm
Show Answer & Explanation
Answer: (d) 1 mm = 0.01 cm
Explanation:
1. 1 m = 1000 mm, so 1 mm = 0.001 m: (a) is correct.
2. 1 kg = 1000 g, so 1 g = 0.001 kg: (b) is correct.
3. 1 m = 100 cm, so 1 cm = 0.01 m: (c) is correct.
4. 1 cm = 10 mm, so 1 mm = \( \frac{1}{10} \) cm = 0.1 cm, not 0.01 cm. So (d) is not correct.
Teacher's Note:
1. Remember the three links: 10 mm = 1 cm, 100 cm = 1 m, 1000 mm = 1 m.
2. Read “not correct” carefully: here we pick the false statement.
Assertion (A): 0.2, 0.20, and 0.200 represent different quantities.
Reason (R): Adding zeros to the right of the last digit after the decimal point does not change the value.
(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: (d) A is false, but R is true.
Explanation:
1. 0.2 = 2 tenths, 0.20 = 20 hundredths = 2 tenths and 0.200 = 200 thousandths = 2 tenths.
2. So all three are the same quantity, and the Assertion is false.
3. The Reason is true: zeros added at the end of the decimal part do not change the value.
4. So the answer is (d) A is false but R is true.
Teacher's Note:
1. When A is false, the answer can only be (d) if R is true.
2. 0.2, 0.20 and 0.200 sit at the same point on the number line.
Assertion (A): 45 paise = 0.45 rupees.
Reason (R): 1 rupee = 100 paise.
(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. Since 1 rupee = 100 paise, 1 paisa = \( \frac{1}{100} \) rupee.
2. So 45 paise = \( \frac{45}{100} \) rupee = ₹0.45. The Assertion is true.
3. The Reason is true, and it is exactly the fact used to change paise into rupees.
4. So the answer is (a).
Teacher's Note:
1. Paise are hundredths of a rupee, just like centimetres are hundredths of a metre.
2. ₹0.45 is read as forty-five paise.
Section B: Short Answer Questions (2 Marks Each)
Question 11. Convert 245 mm into meters. Show the calculation.
Answer:
1 m = 1000 mm, so 1 mm = \( \frac{1}{1000} \) m.
245 mm = \( \frac{245}{1000} \) m.
245 thousandths = 0.245 m.
In simple words: Divide millimetres by 1000 to get metres: 245 mm = 0.245 m.
Teacher's Note:
1. Dividing by 1000 moves the decimal point three places to the left.
2. Check: 0.245 m = 24.5 cm, which is about the length of a ruler and a half.
Question 12. A notebook is 2.45 cm thick. If 10 such notebooks are stacked, what will be the total height in meters?
Answer:
Total height = 10 × 2.45 cm = 24.5 cm (multiplying by 10 moves the point one place right).
1 cm = \( \frac{1}{100} \) m, so 24.5 cm = 24.5 ÷ 100 m.
Total height = 0.245 m.
In simple words: Ten notebooks are 24.5 cm tall, which is 0.245 m.
Teacher's Note:
1. Find the height in cm first, then convert to metres.
2. Multiplying by 10 shifts the point one place right; dividing by 100 shifts it two places left.
Answer:
Write both numbers with three decimal places so the points line up: 15.750 and 8.245.
| 15.750 |
| − 8.245 |
| 7.505 |
Difference = 7.505 kg.
In simple words: 15.750 − 8.245 = 7.505 kg.
Teacher's Note:
1. Add a zero to 15.75 so both numbers have the same number of decimal places.
2. Check by adding back: 7.505 + 8.245 = 15.750.
Question 14. Arrange the following in descending order: 3.045, 3.45, 3.405, 3.054.
Answer:
All numbers have 3 ones, so compare the decimal parts as thousandths: 3.045, 3.450, 3.405, 3.054.
The decimal parts are 045, 450, 405 and 054 thousandths, and 450 > 405 > 054 > 045.
Descending order: 3.45 > 3.405 > 3.054 > 3.045.
In simple words: Make all numbers three-decimal and compare: 3.450, 3.405, 3.054, 3.045.
Teacher's Note:
1. Descending means from the largest to the smallest.
2. Compare tenths first: 3.45 and 3.405 both have 4 tenths, then look at hundredths.
Section C: Short Answer Questions (3 Marks Each)
(a) Find the total cloth sold in three days.
(b) How much more cloth was sold on Tuesday than Wednesday?
Answer:
(a) Line up the decimal points (4.5 = 4.50):
| 3.75 |
| + 4.50 |
| + 2.85 |
| 11.10 |
Total cloth sold = 11.10 m = 11.1 m.
(b) Tuesday − Wednesday = 4.50 − 2.85 = 1.65 m.
So 1.65 m more cloth was sold on Tuesday.
In simple words: The three days add up to 11.1 m, and Tuesday beat Wednesday by 1.65 m.
Teacher's Note:
1. Write 4.5 as 4.50 so that every number has two decimal places.
2. “How much more” always means subtract the smaller from the larger.
(a) 25 hundredths
(b) 4 ones, 3 tenths, and 7 hundredths
(c) 12 tens, 5 tenths
Answer:
(a) 25 hundredths = \( \frac{25}{100} \) = 0.25.
(b) 4 + \( \frac{3}{10} \) + \( \frac{7}{100} \) = 4 + 0.3 + 0.07 = 4.37.
(c) 12 tens = 120 and 5 tenths = 0.5, so the number is 120 + 0.5 = 120.5.
| Number | Hundreds | Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|---|---|
| 0.25 | 0 | . | 2 | 5 | ||
| 4.37 | 4 | . | 3 | 7 | ||
| 120.5 | 1 | 2 | 0 | . | 5 |
In simple words: Put each digit in its place-value column: 0.25, 4.37 and 120.5.
Teacher's Note:
1. 12 tens is 120, not 12; ten tens make a hundred.
2. A place-value table helps to place each digit correctly.
Question 17. A water tank is filled in two stages:
Stage 1: 125.75 litres
Stage 2: 238.8 litres
(a) Find the total volume of water in the tank.
(b) If 150.5 litres of water is removed, find the remaining water.
(c) Convert your final answer into kilolitres.
Answer:
(a) Total = 125.75 + 238.80 = 364.55 litres.
(b) Remaining = 364.55 − 150.50 = 214.05 litres.
(c) 1 kilolitre = 1000 litres, so 214.05 L = 214.05 ÷ 1000 kL = 0.21405 kL.
In simple words: Add the two stages, subtract what was removed, then divide by 1000 for kilolitres.
Teacher's Note:
1. Write 238.8 as 238.80 and 150.5 as 150.50 before adding or subtracting.
2. Dividing by 1000 moves the decimal point three places to the left.
Section D: Long Answer Question (5 Marks)
Roll 1: 15.275 m
Roll 2: 9.65 m
(a) Find the total fabric length.
(b) If 12.5 m was used, how much fabric was left?
(c) Convert the leftover length into centimetres.
(d) If 80 cm of fabric is needed for one shirt, how many shirts can be made?
(e) How much fabric will remain unused after making the shirts?
Answer:
(a) Total = 15.275 + 9.650:
| 15.275 |
| + 9.650 |
| 24.925 |
Total fabric = 24.925 m.
(b) Fabric left = 24.925 − 12.500 = 12.425 m.
(c) 1 m = 100 cm, so 12.425 m = 12.425 × 100 cm = 1242.5 cm.
(d) Each shirt needs 80 cm. 80 × 15 = 1200 cm and 80 × 16 = 1280 cm, which is more than 1242.5 cm.
So the tailor can make 15 shirts.
(e) Fabric used for 15 shirts = 1200 cm, so unused fabric = 1242.5 − 1200 = 42.5 cm (= 0.425 m).
In simple words: 24.925 m bought, 12.425 m (1242.5 cm) left, enough for 15 shirts of 80 cm with 42.5 cm to spare.
Teacher's Note:
1. Only whole shirts can be made, so take the largest whole number of 80 cm pieces that fits.
2. Check: 15 × 80 + 42.5 = 1242.5 cm.
3. Multiplying by 100 moves the decimal point two places to the right.
Section E: Case Study Based Questions (4 Marks Each)
Question 19. During a school science experiment on plant growth, Ritu carefully measured the lengths of three roots she had grown in separate pots. She recorded the measurements as follows:
Root A = 12.45 cm, Root B = 8.3 cm, Root C = 9.85 cm.
(a) Find the total length of the roots in cm and in meters.
(b) Which root is the shortest, and how much shorter is it than the longest root?
(c) Find the average length of the three roots in cm.
(d) Convert the average length into millimetres.
Answer:
(a) Total = 12.45 + 8.30 + 9.85 = 30.6 cm.
In metres: 30.6 ÷ 100 = 0.306 m.
(b) Comparing 12.45, 8.30 and 9.85: the shortest is Root B (8.3 cm) and the longest is Root A (12.45 cm).
Difference = 12.45 − 8.30 = 4.15 cm.
(c) Average = total ÷ number of roots = 30.6 ÷ 3 = 10.2 cm.
(d) 1 cm = 10 mm, so 10.2 cm = 10.2 × 10 = 102 mm.
In simple words: Roots total 30.6 cm (0.306 m), Root B is 4.15 cm shorter than Root A, and the average is 10.2 cm = 102 mm.
Teacher's Note:
1. Average means share the total equally: add all values, then divide by how many there are.
2. Write 8.3 as 8.30 when comparing or subtracting with two-decimal numbers.
Question 20. A skilled carpenter is preparing materials for a custom furniture project. He needs to cut three wooden planks of precise lengths: 1.205 m, 2.5 m, and 0.895 m. Accuracy is crucial to ensure the pieces fit perfectly in the final design.
(a) What is the total wood required?
(b) If the carpenter has only a 5 m long plank, how much wood will remain unused after cutting?
(c) Convert the unused wood into centimetres.
(d) If each small stool requires 0.8 m of wood, how many stools can be made from the unused portion?
Answer:
(a) Total = 1.205 + 2.500 + 0.895 = 4.6 m.
(b) Unused wood = 5.000 − 4.600 = 0.4 m.
(c) 0.4 m = 0.4 × 100 cm = 40 cm.
(d) One stool needs 0.8 m = 80 cm, but only 40 cm is left.
40 cm is only half of 80 cm, so no stool (0 stools) can be made from the unused wood.
In simple words: The planks use 4.6 m, leaving 0.4 m (40 cm), which is not enough for even one 0.8 m stool.
Teacher's Note:
1. Before dividing, check whether the leftover is even enough for one item.
2. Notice 1.205 + 0.895 = 2.1 exactly, which makes the addition quicker.
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Chapter 03 A Peek Beyond the Point Printable Worksheets and Exercises for Class 7 Mathematics
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