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NCERT Solutions for Class 7th Maths Chapter 4 In-text Questions — Division with a Decimal Divisor · Does This Ever End?

Book page 84 – 85 Updated on2026-09-19

Q1.
Example 12: Ravi went from Pune to Matheran by scooter in 2.5 hours. The distance was 126 km. What was his average speed?
Answer

His average speed was 50.4 km per hour.

Average speed = distance ÷ time = 126 ÷ 2.5

The divisor is a decimal, so turn it into a fraction:
126 ÷ 25/10 = 126 × 10/25 = 1260/25

Long division: 25 × 50 = 1250, remainder 10
100 Tenths ÷ 25 = 4 Tenths
= 50.4 km/h
Why it happens: dividing by a fraction is multiplying by its reciprocal. The reciprocal of 25/10 is 10/25, so the dividend gets multiplied by 10 while the divisor becomes the counting number 25. The value of the quotient does not change, because 1260/25 and 126/2.5 are the same fraction written differently.
Check it yourself: 50.4 × 2.5 = 126. ✓ A scooter at about 50 km/h for two and a half hours covering 126 km sounds right.
Q2.
Example 13: Find 4.68 ÷ 1.3. Now, what about 4.68 ÷ 0.13?
Answer

4.68 ÷ 1.3 = 3.6 and 4.68 ÷ 0.13 = 36.

First: 4.68 ÷ 13/10 = 4.68 × 10/13 = 46.8/13
13 × 3 = 39, remainder 7.8 → 78 Tenths ÷ 13 = 6 Tenths
= 3.6

Second: 4.68 ÷ 13/100 = 4.68 × 100/13 = 468/13
13 × 36 = 468
= 36
Why it happens: 0.13 is one-tenth of 1.3. Sharing the same 4.68 into pieces that are ten times smaller gives ten times as many pieces. So the second quotient is ten times the first.
Q3.
What do you notice in these cases?
Answer

When the divisor is a decimal, we can make it a counting number — as long as we do the same to the dividend.

4.68/0.13 = (4.68 × 100)/(0.13 × 100) = 468/13 = 36

The rule: multiply the divisor by 10, 100, 1000 … until it becomes a whole number, multiply the dividend by the same number, and then do ordinary long division.

DivisionMultiply both byBecomesQuotient
126 ÷ 2.5101260 ÷ 2550.4
4.68 ÷ 1.31046.8 ÷ 133.6
4.68 ÷ 0.13100468 ÷ 1336
Why it happens: a division is a fraction, and multiplying the numerator and the denominator of a fraction by the same number gives an equivalent fraction — the same value. So the quotient is untouched, while the divisor becomes friendly enough for long division.
Q4.
Can you calculate 10 ÷ 3? Try dividing using long division. Will this process end?
Answer

No, it never ends. 10 ÷ 3 = 3.333…

Step 1: regroup 1 Ten as 10 Ones. 10 Ones ÷ 3 → 3 Ones, 1 One remains
Step 2: regroup 1 One as 10 Tenths. 10 Tenths ÷ 3 → 3 Tenths, 1 Tenth remains
Step 3: regroup 1 Tenth as 10 Hundredths. 10 Hundredths ÷ 3 → 3 Hundredths, 1 Hundredth remains
Step 4: regroup 1 Hundredth as 10 Thousandths. 10 Thousandths ÷ 3 → 3 Thousandths, 1 Thousandth remains
… and so on for ever.

10 ÷ 3 = 3.333…
Why it happens: every single step ends with a remainder of 1 in the next smaller place. Regrouping that 1 always gives 10 of the next unit, and 10 ÷ 3 always leaves 1 again. Since the step repeats exactly, it can never stop. So 10 ÷ 3 cannot be written with a finite number of decimal digits.
Did you know? This links back to page 76 — 3 is not made of 2s and 5s, so no power of ten is a multiple of 3, and no equivalent fraction over 10, 100 or 1000 exists.
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