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NCERT Solutions for Class 7th Maths Chapter 4 In-text Questions — Decimal Division

Book page 74 – 75 Updated on2026-09-19

Q1.
Example 6: Anuja has a 3.9 m length of ribbon and she wants to cut it into 10 equal pieces. What is the length of each piece in decimal?
Answer

Each piece is 0.39 m long.

3.9 ÷ 10
3.9 = 39/10
Dividing by 10 is the same as multiplying by 1/10:
39/10 ÷ 10 = 39/10 × 1/10 = 39/100
= 0.39 m
Why it happens: the reciprocal of 10 is 1/10, so dividing by 10 multiplies the denominator by 10. The denominator grows from 10 to 100, which is one more zero — so the point slides one more place left, from 3.9 to 0.39.
Check it yourself: ten pieces of 0.39 m give 3.9 m. ✓
Q2.
What is the length of each piece if the ribbon is cut into 100 equal pieces?
Answer

Each piece is 0.039 m long.

3.9 ÷ 100 = 39/10 × 1/100 = 39/1000 = 0.039 m
Why it happens: 100 has two zeroes, so the point moves two places left instead of one. Since 3.9 has only one digit before the point, a zero must be written in to hold the tenths place: 0.039.
Q3.
What is 0.039 m in centimetres and millimetres?
Answer

3.9 cm, which is the same as 39 mm.

1 m = 100 cm, so multiply by 100:
0.039 × 100 = 3.9 cm

1 m = 1000 mm, so multiply by 1000:
0.039 × 1000 = 39 mm
Why it happens: a centimetre is a smaller unit than a metre, so the same length needs a bigger number. Multiplying by 100 moves the point two places right; multiplying by 1000 moves it three places right and the point disappears from view, leaving the whole number 39.
Check it yourself: 39 mm is about the width of three fingers — a believable piece of ribbon after cutting 3.9 m into 100 parts.
Q4.
Complete the table:
Decimal÷ 10÷ 100÷ 1000÷ 10000
18.71.870.1870.01870.00187
21.1    
0.13    
  2.146  
    0.0058
Answer

Move the point left by 1, 2, 3 or 4 places. For the last two rows, work backwards — move the point right.

Decimal÷ 10÷ 100÷ 1000÷ 10000
18.71.870.1870.01870.00187
21.12.110.2110.02110.00211
0.130.0130.00130.000130.000013
214.621.462.1460.21460.02146
585.80.580.0580.0058
Row 4: the number ÷ 100 = 2.146.
So the number = 2.146 × 100 = move the point 2 places right = 214.6

Row 5: the number ÷ 10000 = 0.0058.
So the number = 0.0058 × 10000 = move the point 4 places right = 58
Why it happens: multiplication undoes division. If dividing by 100 moved the point two places left, then getting back to the original number moves it two places right. Once you have the first cell of the row, the rest of the row is just the point sliding one place further left each time.
Q5.
Example 7: Neenu has 29 metres of red ribbon and wants to share it equally with Anu. What is the length of ribbon that each of them will get?
Answer

Each girl gets 14.5 m.

29 ÷ 2
Each gets 14 m, and 1 m is left over.
That 1 m shared between two gives each another 1/2 m.

1/2 = (1 × 5)/(2 × 5) = 5/10 = 0.5

Each girl gets 14 + 0.5 = 14.5 m
Why it happens: a fraction becomes a decimal easily only when its denominator is 10, 100, 1000 and so on. 2 is not one of these, but 2 × 5 = 10, so multiplying the top and bottom by 5 turns 1/2 into 5/10 — the same value, now in a form we can read off the place value chart.
Q6.
How do we convert 1/2 into a decimal?
Answer

Turn the denominator into 10, 100 or 1000 by multiplying the top and the bottom by the same number.

Is 2 a factor of 10? Yes, because 2 × 5 = 10.
1/2 = (1 × 5)/(2 × 5) = 5/10 = 0.5

The same idea handles other denominators:

1/4: 4 × 25 = 100 → 25/100 = 0.25
1/5: 5 × 2 = 10 → 2/10 = 0.2
1/8: 8 × 125 = 1000 → 125/1000 = 0.125
Why it happens: the decimal system only has places worth tenths, hundredths, thousandths … So a fraction can be written as a decimal in the direct way only when it can be re-dressed with one of those denominators. Multiplying top and bottom by the same number never changes the value — it only changes the clothes.
Tip: denominators like 2, 4, 5, 8, 20, 25 and 50 all work, because they are built only from 2s and 5s — and 10 = 2 × 5.
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