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NCERT Solutions for Class 7th Maths Chapter 4 Figure it Out — Decimal Multiplication

Book page 73 – 74 Updated on2026-09-19

Q1.
Recall that a tenth is 0.1, a hundredth is 0.01, and so on. Find the following products in tenths, hundredths and so on: (a) 6 × 4 tenths = 24 tenths (b) 7 × 0.3 (c) 9 × 5 hundredths
Answer

Count the pieces first, then name the piece.

(a) 6 × 4 tenths = 24 tenths = 24/10 = 2.4

(b) 0.3 is 3 tenths.
7 × 3 tenths = 21 tenths = 21/10 = 2.1

(c) 9 × 5 hundredths = 45 hundredths = 45/100 = 0.45
Why it happens: "tenth" and "hundredth" behave like units. Six lots of 4 tenths is 24 tenths, just as six lots of 4 pencils is 24 pencils. Then 24 tenths is more than 2 whole ones, because 10 tenths make 1, so 24 tenths = 2 wholes and 4 tenths = 2.4.
Tip: the unit tells you the denominator. Tenths → over 10, hundredths → over 100.
Q2.
Find the products: (a) 27.34 × 6 (b) 4.23 × 3.7 (c) 0.432 × 0.23
Answer

Drop the points, multiply, then count the places.

(a) 2734 × 6 = 16404
Places: 2 + 0 = 2 → 164.04

(b) 423 × 37 = 15651
Places: 2 + 1 = 3 → 15.651

(c) 432 × 23 = 9936
Places: 3 + 2 = 5, but 9936 has only 4 digits, so pad one zero in front → 0.09936
Why it happens: in (c) the fractions are 432/1000 and 23/100, so the denominator is 100000 — five zeroes. The numerator 9936 must therefore be written as 09936 before the point goes in front of it.
Check it yourself: (c) multiplies two numbers that are both less than 1, so the answer must be smaller than both. 0.09936 is indeed smaller than 0.432 and smaller than 0.23.
Q3.
Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Answer

4.95 m of cloth is needed.

Cloth for 3 shirts = 1.65 × 3
165 × 3 = 495
Places: 2 + 0 = 2
= 4.95 m
Why it happens: 1.65 m is 1 m 65 cm. Three shirts need 3 m and 195 cm; 195 cm is 1 m 95 cm, so the total is 4 m 95 cm = 4.95 m.
Q4.
Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹15.50 and each eraser was ₹2.75. How much did she spend in all?
Answer

Meenu spent ₹70.25.

Notebooks: 15.50 × 4
1550 × 4 = 6200, places 2 + 0 = 2 → ₹62.00

Erasers: 2.75 × 3
275 × 3 = 825, places 2 + 0 = 2 → ₹8.25

Total = 62.00 + 8.25 = ₹70.25
Why it happens: the two items cost different amounts, so each group is multiplied on its own and only then added. Adding first would mix up rupees per notebook with rupees per eraser.
Check it yourself: ₹15.50 is a little over ₹15, so 4 books are a little over ₹60. Erasers add about ₹8. The total should be a little over ₹68 — and ₹70.25 is.
Q5.
The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by placing 36 rupee coins one over the other? Write the answer in centimeters.
Answer

The stack is 5.22 cm tall.

Height = 1.45 × 36 mm
145 × 36 = 5220
Places: 2 + 0 = 2 → 52.20 mm

1 cm = 10 mm, so divide by 10:
52.2 ÷ 10 = 5.22 cm
Why it happens: changing mm to cm means dividing by 10, and dividing by 10 slides the point one place left. So 52.2 mm becomes 5.22 cm.
Check it yourself: 145 × 36 = 145 × 30 + 145 × 6 = 4350 + 870 = 5220. ✓
Q6.
Math Talk: The price of 1 kg of oranges is ₹56.50. What is the price of 2.250 kg of oranges? Can we write 56.50 as 56.5 and 2.250 as 2.25 and multiply? Will we get the same product? Why?
Answer

The price is ₹127.125, and yes — dropping the last zeroes gives exactly the same product.

As printed: 5650 × 2250 = 12712500
Places: 2 + 3 = 5 → 127.12500

Shortened: 565 × 225 = 127125
Places: 1 + 2 = 3 → 127.125

Both answers are the same number: 127.12500 = 127.125.

Why it happens: a zero at the end of a decimal adds no value. 56.50 = 5650/100 = 565/10, and 2.250 = 2250/1000 = 225/100. The fractions are equal, so the products must be equal. Each zero you drop from a number removes one zero from its denominator — and so removes one decimal place from the product. The two changes cancel out exactly.
Tip: a zero before the first significant digit is different. In 0.05 the zero is holding the tenths place, so it cannot be dropped.
Q7.
Dwarakanath purchases notebooks at a wholesale price of ₹23.6 per piece and sells each notebook at ₹30/-. How much profit does he make if he sells 50 books in a week?
Answer

His profit is ₹320.

Profit on one notebook = 30 − 23.6 = ₹6.4
Profit on 50 notebooks = 6.4 × 50
64 × 50 = 3200, places 1 + 0 = 1 → ₹320

The longer route gives the same answer:

Cost price of 50 books = 23.6 × 50 = ₹1180
Selling price of 50 books = 30 × 50 = ₹1500
Profit = 1500 − 1180 = ₹320 ✓
Why it happens: profit per book multiplied by the number of books gives the same total as total selling price minus total cost price. Both are the same subtraction, done before or after multiplying.
Q8.
Given that 18 × 12 = 216, find the products: (a) 18 × 1.2 (b) 18 × 0.12 (c) 1.8 × 1.2 (d) 0.18 × 0.12 (e) 0.018 × 0.012 (f) 1.8 × 12. In which of the cases above is the product less than 1?
Answer

The digits are always 216. Only the position of the point changes.

ProductDecimal placesAnswer
(a)18 × 1.20 + 1 = 121.6
(b)18 × 0.120 + 2 = 22.16
(c)1.8 × 1.21 + 1 = 22.16
(d)0.18 × 0.122 + 2 = 40.0216
(e)0.018 × 0.0123 + 3 = 60.000216
(f)1.8 × 121 + 0 = 121.6

The product is less than 1 in (d) and (e).

Why it happens: in (d) and (e) both numbers are smaller than 1, so each one shrinks the other. Everywhere else at least one number is bigger than 1. In (e) the answer needs 6 decimal places but 216 has only 3 digits, so three zeroes are written in front: 0.000216.
Tip: (b) and (c) give the same answer. Moving a point one place left in one factor and one place right in the other leaves the product unchanged, because you have divided by 10 and multiplied by 10.
Q9.
In which of the following multiplications is the product less than 1? Can you find the answer without actually doing the multiplications? (a) 7 × 0.6 (b) 0.7 × 0.6 (c) 0.7 × 6 (d) 0.07 × 0.06
Answer

The product is less than 1 in (b) and (d).

You can decide without multiplying: a product is less than 1 only when both numbers are less than 1.

MultiplicationBoth less than 1?ProductLess than 1?
(a)7 × 0.6No (7 > 1)4.2No
(b)0.7 × 0.6Yes0.42Yes
(c)0.7 × 6No (6 > 1)4.2No
(d)0.07 × 0.06Yes0.0042Yes
Why it happens: if both numbers are below 1, then taking a part of a part gives something even smaller — smaller than each of them, and so certainly below 1. But be careful: "one number below 1" is not enough. In (a), 0.6 of 7 is still 4.2, because 7 is large enough to survive being cut down.
Q10.
Multiplying the following numbers by 10, 100 and 1000 to complete the table.
 × 10× 100× 1000
5.7   
23.02   
0.92   
0.306   
24.67   
Answer

Multiplying by 10, 100 or 1000 moves the point right by 1, 2 or 3 places.

Number× 10× 100× 1000
5.7575705700
23.02230.2230223020
0.929.292920
0.3063.0630.6306
24.67246.7246724670
Why it happens: multiplying by 10 makes every digit worth ten times as much. A Tenths digit becomes a Ones digit, a Ones digit becomes a Tens digit. Sliding the point one place right does that to all the digits at once. Once the point reaches the end of the digits, extra zeroes appear to hold the empty places — that is why 0.92 × 1000 is 920 and not 92.
Tip: this is the exact opposite of the division rule on page 68. Division moves the point left, multiplication moves it right, and the number of zeroes tells you how far.
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