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

Book page 73 Updated on2026-09-05

Q1.
Why can we stop comparing at this point? Can we be sure that whatever digits are there after this will not affect our conclusion?
Answer

Yes, we can stop, and yes, we can be sure.

At the hundredths place, 6.465 has 1 hundredth more than 6.456.
1 hundredth = 10 thousandths
The most that all the remaining places of 6.456 can add is 0.00999… < 0.01
So the lead of one hundredth can never be caught up.
Why it happens: each place is worth ten times everything that can follow it added together. Once one number leads at some place, no combination of smaller places can reverse the result — the same reason 500 > 499 no matter what digits we add.
Tip: this is exactly how names are ordered in a dictionary — the first letter that differs settles it, and the rest of the word does not matter.
Q2.
Which decimal number is greater? (a) 1.23 or 1.32 (b) 3.81 or 13.800 (c) 1.009 or 1.090
Answer
ComparisonFirst differenceGreater
(a) 1.23 , 1.32units 1 = 1; tenths 2 vs 3tenths1.32
(b) 3.81 , 13.8003 has 0 tens, 13 has 1 tentens13.800
(c) 1.009 , 1.090units and tenths 0 = 0; hundredths 0 vs 9hundredths1.090
Why it happens: in (b) do not be misled by the three decimal places of 13.800 — the whole-number parts settle it at once, 13 > 3. In (c), 1.009 is nine thousandths above 1 while 1.090 is ninety thousandths above 1, so 1.090 wins by a factor of ten.
Q3.
Which of the above is closest to 1.09?
Answer

The numbers were 0.9, 1.1, 1.01 and 1.11. Find each distance from 1.09.

NumberDistance from 1.09
0.91.09 – 0.90 = 0.19
1.11.10 – 1.09 = 0.01
1.011.09 – 1.01 = 0.08
1.111.11 – 1.09 = 0.02
Smallest distance = 0.01, so 1.1 is closest to 1.09.
Why it happens: "closest" means smallest difference, not smallest number. Writing every number with the same two decimal places (0.90, 1.10, 1.01, 1.11) makes the subtraction easy and safe.
Q4.
Which among these is closest to 4: 3.56, 3.65, 3.099?
Answer
NumberDistance from 4
3.564 – 3.56 = 0.44
3.654 – 3.65 = 0.35
3.0994 – 3.099 = 0.901
3.65 is closest to 4.
Why it happens: all three are below 4, so the biggest of them is the nearest. 3.65 > 3.56 because 6 tenths beats 5 tenths, and 3.099 has only 0 tenths, putting it far behind.
Q5.
Which among these is closest to 1: 0.8, 0.69, 1.08?
Answer
NumberDistance from 1
0.81 – 0.8 = 0.2
0.691 – 0.69 = 0.31
1.081.08 – 1 = 0.08
1.08 is closest to 1.
Why it happens: here the nearest number lies above 1, not below it. Distance is measured in both directions, so always compare the actual gaps rather than guessing from the size of the numbers.
Q6.
In each case below use the digits 4, 1, 8, 2, and 5 exactly once and try to make a decimal number as close as possible to 25.
Answer

The shape of the boxes fixes how many digits sit before the decimal point, so each row has a different best answer.

Box patternBest numberDistance from 25
□□.□□□25.1480.148
□.□□□8.54216.458
□□□.□□124.5899.58
Row 1: the whole-number part can be 24 or 25.
Best above: 25.148 → gap 0.148
Best below: 24.851 → gap 0.149
So 25.148 wins, but only just.

Row 2: only one digit before the point, so the largest possible number is 8.542.

Row 3: three digits before the point, so the smallest possible number is 124.58.
Why it happens: in row 1 we can actually reach 25, so we make the fractional part as small as we can — 1, 4, 8 in that order. In rows 2 and 3 the target 25 is out of reach, so we go as high (or as low) as the digits allow.
Check it yourself: 24.851 misses by 0.149 and 25.148 misses by 0.148 — a difference of just one thousandth. Always compare both sides before deciding.
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