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

Book page 86 – 87 Updated on2026-09-19

Q1.
Express the following fractions in decimal form: (a) 2/5 (b) 13/4 (c) 4/50 (d) 5/8
Answer

Build a denominator of 10, 100 or 1000 in each case.

(a) 5 × 2 = 10 → 2/5 = 4/10 = 0.4

(b) 4 × 25 = 100 → 13/4 = 325/100 = 3.25

(c) 50 × 2 = 100 → 4/50 = 8/100 = 0.08

(d) 8 × 125 = 1000 → 5/8 = 625/1000 = 0.625
Why it happens: every one of these denominators — 5, 4, 50, 8 — is made only of 2s and 5s, so each of them divides some power of ten. The number of decimal places you need is decided by how big that power of ten has to be: 10 for (a), 100 for (b) and (c), 1000 for (d).
Check it yourself: 13/4 is 3 wholes and 1/4 left over, and a quarter is 0.25. So 3.25. ✓
Q2.
Find the quotients: (a) 24.86 ÷ 1.2 (b) 5.728 ÷ 1.52
Answer

First clear the decimal from the divisor, then divide. Neither of these quotients ends.

(a) 24.86 ÷ 1.2 = (24.86 × 10)/(1.2 × 10) = 248.6 ÷ 12
12 × 20 = 240, remainder 8.6
86 Tenths ÷ 12 → 7 Tenths, 2 Tenths remain
20 Hundredths ÷ 12 → 1 Hundredth, 8 Hundredths remain
80 Thousandths ÷ 12 → 6 Thousandths, 8 Thousandths remain … the 8 keeps coming back
= 20.7166… (the 6 repeats for ever) ≈ 20.72

(b) 5.728 ÷ 1.52 = (5.728 × 100)/(1.52 × 100) = 572.8 ÷ 152
152 × 3 = 456, remainder 116.8
Carrying on: 3.7684210526315789473…
= 3.7684… ≈ 3.77
Why it happens: after clearing the divisors we are dividing by 12 = 2 × 2 × 3 and by 152 = 2 × 2 × 2 × 19. The extra factors 3 and 19 are not 2s or 5s, so no power of ten is a multiple of them, and the division cannot stop. As on page 85, a remainder repeats and drags the digits round with it.
Tip: when a quotient does not end, say how far you have gone. Two decimal places is usually enough for a practical answer.
Q3.
Evaluate the following using the information 156 × 12 = 1872. (a) 15.6 × 1.2 = (b) 187.2 ÷ 1.2 = (c) 18.72 ÷ 15.6 = (d) 0.156 × 0.12 =
Answer

The digits are always 156, 12 and 1872. Only the point moves.

(a) 15.6 × 1.2: places 1 + 1 = 2 → 18.72

(b) 187.2 ÷ 1.2 = 1872 ÷ 12 = 156
  (both multiplied by 10)

(c) 18.72 ÷ 15.6 = 1872 ÷ 1560 = 1.2
  (both multiplied by 100)

(d) 0.156 × 0.12: places 3 + 2 = 5 → 0.01872
Why it happens: multiplication and division are opposites. Since 15.6 × 1.2 = 18.72, we already know 18.72 ÷ 1.2 = 15.6 and 18.72 ÷ 15.6 = 1.2 without dividing at all. For (b), 187.2 is ten times 18.72, so its quotient is ten times 15.6 — that is, 156.
Check it yourself: 1.2 × 156 = 187.2. ✓
Q4.
Evaluate the following: (a) 25 ÷ ______ = 0.025 (b) 25 ÷ ______ = 250 (c) 25 ÷ ______ = 2.5 (d) 25 ÷ 10 = 25 × _____ (e) 25 ÷ 0.10 = 25 × ______ (f) 25 ÷ 0.01 = 25 × ______
Answer
(a) 25 → 0.025: the point moved 3 places left, so divide by 1000

(b) 25 → 250: the answer is bigger, so the divisor is below 1. 25 ÷ 0.1 = 250

(c) 25 → 2.5: the point moved 1 place left, so divide by 10

(d) 25 ÷ 10 = 25 × 0.1  (that is, 1/10)

(e) 25 ÷ 0.10 = 25 × 10

(f) 25 ÷ 0.01 = 25 × 100
Why it happens: dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 10 is 0.1, and the reciprocal of 0.1 is 10. This is why (d) and (e) point in opposite directions even though both involve a 10 and a 0.1. In (f), 0.01 is one hundredth, and there are 100 hundredths in each whole — so 25 wholes hold 2500 of them.
Check it yourself: 25 ÷ 0.01 = 2500, and 25 × 100 = 2500. ✓
Q5.
Find the quotient: (a) 2.46 ÷ 1.5 = (b) 2.46 ÷ 0.15 = (c) 2.46 ÷ 0.015 = Is the quotient obtained in 24.6 ÷ 1.5 the same as the quotient obtained in 2.46 ÷ 0.15?
Answer
(a) 2.46 ÷ 1.5 = 24.6 ÷ 15 = 1.64

(b) 2.46 ÷ 0.15 = 246 ÷ 15 = 16.4

(c) 2.46 ÷ 0.015 = 2460 ÷ 15 = 164

Yes, 24.6 ÷ 1.5 gives the same quotient as 2.46 ÷ 0.15.

24.6 ÷ 1.5 = 246 ÷ 15 = 16.4
2.46 ÷ 0.15 = 246 ÷ 15 = 16.4 ✓
Why it happens: both divisions become 246 ÷ 15 once the divisor is cleared. Going from 24.6 ÷ 1.5 to 2.46 ÷ 0.15 divides the dividend by 10 and the divisor by 10. Making both ten times smaller leaves the quotient exactly where it was — the pieces shrank, but so did the whole.
Tip: in (a), (b), (c) only the divisor shrinks. Ten times smaller pieces means ten times as many of them, so each quotient is ten times the one before.
Q6.
A 4 m long wooden block has to be cut into 5 pieces of equal length. What is the length of each piece?
Answer

Each piece is 0.8 m long, that is 80 cm.

4 ÷ 5 = 4/5 = (4 × 2)/(5 × 2) = 8/10 = 0.8 m
Why it happens: 4 whole metres cannot be shared into 5 equal whole metres, so we regroup: 4 Ones become 40 Tenths, and 40 Tenths ÷ 5 = 8 Tenths each. Eight tenths of a metre is 0.8 m.
Check it yourself: 0.8 × 5 = 4. ✓
Q7.
If the perimeter of a regular polygon with 12 sides is 208.8 cm, what is the length of its side?
Answer

Each side is 17.4 cm.

In a regular polygon all sides are equal.
Side = perimeter ÷ number of sides = 208.8 ÷ 12

12 × 17 = 204, remainder 4.8
48 Tenths ÷ 12 = 4 Tenths
= 17.4 cm
Why it happens: the perimeter is the total distance round the shape. Since the 12 sides are all the same length, sharing the perimeter equally among them gives one side.
Check it yourself: 17.4 × 12 = 208.8. ✓
Q8.
3 litres of watermelon juice is shared among 8 friends equally. How much watermelon juice will each get? Express the quantity of juice in millilitres.
Answer

Each friend gets 0.375 litres, which is 375 ml.

3 ÷ 8 = 3/8
8 × 125 = 1000, so 3/8 = 375/1000 = 0.375 l

1 l = 1000 ml, so multiply by 1000:
0.375 × 1000 = 375 ml
Why it happens: 3 whole litres split among 8 gives less than one litre each, so the answer must be below 1. Regrouping 3 Ones as 30 Tenths gives 3 Tenths each with 6 Tenths left, then 60 Hundredths gives 7 each with 4 left, then 40 Thousandths gives 5 each — 0.375, exactly what the fraction method gave.
Check it yourself: 375 × 8 = 3000 ml = 3 l. ✓
Q9.
A car covers 234.45 km using 12.6 litres of petrol. What is the distance travelled per litre?
Answer

The car travels about 18.61 km per litre.

Distance per litre = 234.45 ÷ 12.6
Clear the divisor — multiply both by 10:
= 2344.5 ÷ 126

126 × 18 = 2268, remainder 76.5
765 Tenths ÷ 126 → 6 Tenths, 9 Tenths remain
90 Hundredths ÷ 126 → 0, 90 remain
900 Thousandths ÷ 126 → 7, 18 remain …
= 18.6071… ≈ 18.61 km per litre
Why it happens: this quotient does not end, because after clearing the divisor we are dividing by 126 = 2 × 3 × 3 × 7, and the 3s and the 7 are not factors of any power of ten. For a real answer about petrol, two decimal places is plenty.
Check it yourself: 18.6 × 12.6 = 234.36 km, just short of 234.45 — so a shade more than 18.6 is right.
Q10.
13.5 kg of flour (aata) was distributed equally among 15 students. How much flour did each student receive?
Answer

Each student received 0.9 kg, that is 900 g.

13.5 ÷ 15
13 Ones ÷ 15 → 0 Ones. Place the point.
Regroup 13 Ones as 130 Tenths; with the 5 Tenths → 135 Tenths
135 Tenths ÷ 15 = 9 Tenths each
= 0.9 kg
Why it happens: 13.5 is less than 15, so each share must be less than 1 kg. The quotient starts with 0 in the Ones place, and the first real digit appears in the Tenths place.
Check it yourself: 0.9 × 15 = 13.5. ✓
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