NCERT Solutions Ganita Prakash (Part 1) Chapter 3 In-text Questions — Locating and Comparing Decimals

Book page 72 Updated on2026-09-05

Q1.

Using similar reasoning find out the decimal numbers in the boxes below.

Answer

First find the size of one division on each number line, then count divisions.

First line (8 to 8.1, 10 divisions):

Size of one division = 0.1 ÷ 10 = 0.01
d is at the 1st division → 8 + 0.01 = 8.01
e is at the 5th division → 8 + 5 × 0.01 = 8.05

Second line (4.3 to 4.8, 10 divisions):

Size of one division = 0.5 ÷ 10 = 0.05
f is at the 1st division → 4.3 + 0.05 = 4.35
g is at the 4th division → 4.3 + 4 × 0.05 = 4.5
h is at the 11th division → 4.3 + 11 × 0.05 = 4.85

Why it happens: the marks look identical on both lines, but they stand for different amounts — 0.01 on the first and 0.05 on the second. The value of a division is (labelled gap) ÷ (number of parts), and that must be worked out every time.

Tip: h lies one division beyond the 4.8 mark, so it is 4.8 + 0.05 = 4.85.

Q2.

Which is larger: 6.456 or 6.465?

Answer

6.465 is larger. Compare digit by digit, starting from the highest place value.

Place	6.456	6.465	Decision
Units	6	6	same — go on
Tenths	4	4	same — go on
Hundredths	5	6	5 < 6 → 6.465 is larger
Thousandths	6	5	never reached

Why it happens: both numbers agree up to the tenths, so the contest is decided in the hundredths place. One hundredth is worth 10 thousandths, so the extra hundredth in 6.465 can never be beaten by the thousandths digit of 6.456 — the biggest a thousandths digit can be is 9, which is still less than 10.

Check it yourself: 6.465 – 6.456 = 0.009, so the gap is nine thousandths.

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