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

Book page 71 Updated on2026-09-05

Q1.
Can you tell which of these is the smallest and which is the largest?
Answer

Comparing 0.2, 0.20, 0.200, 0.02 and 0.002:

0.2 = 0.20 = 0.200 = 200⁄1000
0.02 = 20⁄1000
0.002 = 2⁄1000
Order: 0.002 < 0.02 < 0.2 = 0.20 = 0.200
Largest: 0.2 (= 0.20 = 0.200)    Smallest: 0.002
Why it happens: writing all five with three decimal places makes them easy to compare — 200, 20 and 2 thousandths. The largest is ten times the next one and a hundred times the smallest.
Q2.
Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
Answer
NumberUnitsTenthsHundredthsThousandths
4.54500
4.054050
0.4050405
4.0504050
4.504500
4.0054005
04.504500
4.5 = 4.50 = 04.50
4.05 = 4.050
0.405 and 4.005 are different from all the others.
Why it happens: zeros at the two ends — before the first digit or after the last — are only decoration. Zeros between digits are not: the 0 in 4.05 keeps the 5 in the hundredths place, and the two 0s in 4.005 push the 5 all the way to the thousandths place.
Q3.
Identify the decimal number in the last number line in Figure (b) denoted by ‘?’.
Answer

Follow the magnifications one level at a time.

Level 1: the box lies between 3 and 4 → the number starts with 3
Level 2 (3 to 4): the box lies between 3.0 and 3.1 → 3.0…
Level 3 (3.0 to 3.1): the box lies between 3.05 and 3.06 → 3.05…
Level 4 (3.05 to 3.06): the arrow is on the 9th of 10 marks
? = 3.05 + 9 × 0.001 = 3.059
Why it happens: each magnification cuts the previous gap into 10 equal parts, so each level fixes one more decimal digit — first the units, then the tenths, then the hundredths, then the thousandths.
Tip: compare with Figure (a), where the same four levels zoom in on 4.185: 4 → 4.1 → 4.18 → 4.185.
Q4.
Make such number lines for the decimal numbers: (a) 9.876 (b) 0.407.
Answer

Draw four number lines, each one magnifying a part of the one above it.

Level(a) for 9.876(b) for 0.407
10 to 10, mark the part between 9 and 100 to 10, mark the part between 0 and 1
29 to 10 in tenths, mark 9.8 to 9.90 to 1 in tenths, mark 0.4 to 0.5
39.8 to 9.9 in hundredths, mark 9.87 to 9.880.4 to 0.5 in hundredths, mark 0.40 to 0.41
49.87 to 9.88 in thousandths, arrow on the 6th mark → 9.8760.40 to 0.41 in thousandths, arrow on the 7th mark → 0.407
010 zoom into 9 – 10 910 zoom into 9.8 – 9.9 9.879.88 9.876 Each line magnifies the marked part of the line above it.
Zooming in on 9.876 — the same four-step magnification used in the book's Figure (a).
Why it happens: a decimal number is located by trapping it between two marks, then splitting that gap into 10 and trapping it again. Each split reveals the next digit.
Q5.
In the number line shown below, what decimal numbers do the boxes labelled ‘a’, ‘b’, and ‘c’ denote? The box with ‘b’ corresponds to the decimal number 7.5; are you able to see how? … What numbers do ‘a’ and ‘c’ denote?
Answer

There are 5 units between 5 and 10, and the gap is cut into 10 equal parts.

Size of each division = 5 ÷ 10 = 1⁄2 unit = 0.5

a is at the 2nd division → 5 + 2 × 0.5 = 6
b is at the 5th division → 5 + 5 × 0.5 = 7.5 ✓
c is at the 9th division → 5 + 9 × 0.5 = 9.5
Why it happens: the number of divisions does not have to match the number of units. Here every two divisions make one unit, so each single division is half a unit — 0.5. Always work out the size of one division before reading any mark.
Check it yourself: from 5, counting 0.5 at a time gives 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10 — ten steps, landing exactly on 10.
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