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NCERT Solutions Ganita Prakash (Part 1) Chapter 3 –80Chapter-end exercise — Figure it Out

Book page 78 Updated on2026-09-05

Q1.
Convert the following fractions into decimals: (a) 5/100 (b) 16/1000 (c) 12/10 (d) 254/1000
Answer
FractionPlace value splitDecimal
(a)5⁄1000 units, 0 tenths, 5 hundredths0.05
(b)16⁄100010⁄1000 + 6⁄1000 = 1⁄100 + 6⁄10000.016
(c)12⁄1010⁄10 + 2⁄10 = 1 + 2⁄101.2
(d)254⁄10002⁄10 + 5⁄100 + 4⁄10000.254
Why it happens: the denominator tells you how many places to leave after the point — one zero for tenths, two for hundredths, three for thousandths. Count the digits in the numerator and pad with zeros on the left if needed, as in (a) and (b).
Q2.
Convert the following decimals into a sum of tenths, hundredths and thousandths: (a) 0.34 (b) 1.02 (c) 0.8 (d) 0.362
Answer
(a) 0.34 = 3⁄10 + 4⁄100

(b) 1.02 = 1 + 0⁄10 + 2⁄100 = 1 + 2⁄100  (also 100⁄100 + 2⁄100)

(c) 0.8 = 8⁄10

(d) 0.362 = 3⁄10 + 6⁄100 + 2⁄1000
Why it happens: each digit after the point is multiplied by its own place value — the first by 1⁄10, the second by 1⁄100, the third by 1⁄1000. In (b) the tenths digit is 0, so that term simply disappears.
Q3.
What decimal number does each letter represent in the number line below?
Answer

The labelled marks 6.4, 6.5 and 6.6 are one tenth apart, and each tenth has been split into 4 equal divisions.

Size of one division = 0.1 ÷ 4 = 0.025

a is 2 divisions after 6.4 → 6.4 + 2 × 0.025 = 6.45
c is 1 division after 6.5 → 6.5 + 0.025 = 6.525
b is 2 divisions after 6.5 → 6.5 + 2 × 0.025 = 6.55
Why it happens: do not assume there are always 10 divisions. Count them first: here only 3 small marks appear between 6.4 and 6.5, making 4 parts, so each part is a quarter of a tenth = 0.025.
Check it yourself: 6.4, 6.425, 6.45, 6.475, 6.5 — four steps of 0.025 land exactly on 6.5. ✓
Q4.
Arrange the following quantities in descending order: (a) 11.01, 1.011, 1.101, 11.10, 1.01 (b) 2.567, 2.675, 2.768, 2.499, 2.698 (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m
Answer

Give every number the same number of decimal places, then compare from the left.

Written to the same placesDescending order
(a)11.010, 1.011, 1.101, 11.100, 1.01011.10, 11.01, 1.101, 1.011, 1.01
(b)2.567, 2.675, 2.768, 2.499, 2.6982.768, 2.698, 2.675, 2.567, 2.499
(c)4.678, 4.595, 4.600, 4.656, 4.6664.678 g, 4.666 g, 4.656 g, 4.600 g, 4.595 g
(d)33.130, 33.310, 33.133, 33.331, 33.31333.331 m, 33.313 m, 33.31 m, 33.133 m, 33.13 m
Why it happens: in (a) the whole-number part settles the first two places — 11 beats 1. In (d) all five have the same whole part 33 and the same first decimal digit choices, so the ordering is decided in the hundredths and thousandths places: 33.310 > 33.133 because 3 tenths beats 1 tenth.
Tip: padding with zeros (33.31 → 33.310) never changes a value but makes the columns line up, which is the safest way to compare.
Q5.
Using the digits 1, 4, 0, 8, and 6 make: (a) the decimal number closest to 30 (b) the smallest possible decimal number between 100 and 1000.
Answer

(a) No arrangement gives 30 exactly (there is no digit 3), so check the closest candidates on both sides.

CandidateValueDistance from 30
Largest starting with 1818.64011.360
Smallest starting with 4040.16810.168
Largest single-digit whole part8.641021.359
The smallest number above 30 is 40.168, at a distance of 10.168.
The largest number below 30 is 18.640, at a distance of 11.360.
So 40.168 is closest to 30.

(b) To be between 100 and 1000 the number needs a 3-digit whole part, leaving 2 digits after the point.

Smallest 3-digit whole part from 1, 4, 0, 8, 6 (cannot start with 0) = 104
Remaining digits 6 and 8 → smallest fractional part = .68
Answer: 104.68
Why it happens: to make a number small, put the smallest available digit in the biggest place — but never a 0 at the very front, or the number loses a place value and drops below 100.
Q6.
Will a decimal number with more digits be greater than a decimal number with fewer digits?
Answer

No. The number of digits says nothing about the size.

PairMore digitsWhich is greater
2.05 and 2.52.052.5 is greater
0.9 and 0.12340.12340.9 is greater
7.000 and 77.000they are equal
13.8 and 3.88883.888813.8 is greater
Why it happens: every digit after the decimal point stands for a smaller piece — tenths, then hundredths, then thousandths. Adding more of them can only make tiny additions, so a long string of small pieces can never beat a bigger digit in a higher place.
Tip: always compare place by place from the left, never by counting digits.
Q7.
Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums, and 0.05 kg of ginger. Calculate the total weight of the items she bought.
Answer
Write everything to two decimal places:
0.25 + 0.30 + 0.50 + 0.20 + 0.05
Hundredths: 5 + 0 + 0 + 0 + 5 = 10 → 0, carry 1
Tenths: 2 + 3 + 5 + 2 + 0 + 1 = 13 → 3, carry 1
Units: 0 + 1 = 1
Total = 1.30 kg = 1 kg 300 g
Why it happens: the hundredths make one whole tenth, and the 13 tenths then make one whole kilogram with 3 tenths left over — two regroupings in one small sum.
Check it yourself: in grams — 250 + 300 + 500 + 200 + 50 = 1300 g = 1.3 kg ✓
Q8.
Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk to a milk dairy in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity of milk supplied to the dairy in the last three days.
Answer
First three days = 3.79 + 4.20 + 4.25
Hundredths: 9 + 0 + 5 = 14 → 4, carry 1
Tenths: 7 + 2 + 2 + 1 = 12 → 2, carry 1
Units: 3 + 4 + 4 + 1 = 12
First three days = 12.24 L

Last three days = 25 – 12.24
= 25.00 – 12.24
= 12.76 L
Why it happens: the 6-day total is fixed at 25 L, so whatever is not supplied in the first three days must come in the last three. Writing 25 as 25.00 keeps the columns aligned for the subtraction.
Check it yourself: 12.24 + 12.76 = 25.00 ✓ Pinto supplied slightly more milk in the second half of the week.
Q9.
Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
Answer
February weight – January weight = 34.50 – 35.75 < 0
So Tinku has lost weight.

Change = 35.75 – 34.50
Hundredths: 5 – 0 = 5
Tenths: 7 – 5 = 2
Units: 35 – 34 = 1
= 1.25 kg
Why it happens: 34.50 is less than 35.75 because the whole parts differ at once — 34 < 35. The loss of 1.25 kg is 1 kg and 250 g.
Check it yourself: 34.50 + 1.25 = 35.75 ✓
Q10.
Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ____, _____
Answer

Look at the changes between consecutive terms.

5.5 → 6.4 : + 0.9
6.4 → 6.39 : – 0.01
6.39 → 7.29 : + 0.9
7.29 → 7.28 : – 0.01
So the rule alternates + 0.9 and – 0.01.

Continuing the rule from 7.28:

7.28 + 0.9 = 8.18
8.18 – 0.01 = 8.17
8.17 + 0.9 = 9.07
9.07 – 0.01 = 9.06
Pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, 9.07, 9.06
Why it happens: adding 0.9 is the same as "add 1, subtract 0.1", and subtracting 0.01 nudges only the hundredths digit. Running the pair of moves together raises the number by 0.89 in each round.
Tip: the sixth and seventh terms are printed as 6.18 and 6.17. Following the pattern they should read 8.18 and 8.17 — the book's own answer key also continues from 8.17, giving 9.07 and 9.06. (If you insist on taking 6.17 as printed, the same alternating rule gives 7.07 and 7.06.)
Q11.
How many millimeters make 1 kilometer?
Answer
1 km = 1000 m
1 m = 100 cm and 1 cm = 10 mm, so 1 m = 1000 mm
1 km = 1000 × 1000 mm
= 10,00,000 mm (ten lakh, or one million, millimetres)
Why it happens: each step of the metric ladder is a factor of 10 — km → m is ×1000, m → mm is ×1000 again, so km → mm is ×10,00,000.
Tip: read it the other way too — 1 mm = 1⁄10,00,000 km = 0.000001 km.
Q12.
Indian Railways offers optional travel insurance for passengers who book e-tickets. It costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
Answer
Cost per passenger = 45 paise = ₹0.45
Number of passengers = 1 lakh = 1,00,000
Total = 0.45 × 1,00,000
= 45 × 1000
= ₹45,000

Working in paise instead:

45 × 1,00,000 = 45,00,000 paise
45,00,000 ÷ 100 = ₹45,000
Why it happens: multiplying by 1,00,000 shifts the decimal point five places to the right: 0.45 → 45000.0. A charge that looks tiny per person becomes a large amount over a lakh of passengers.
Did you know? Indian Railways carries well over two crore passengers a day, so even fractions of a rupee add up very quickly.
Q13.
Which is greater? (a) 10/1000 or 1/10 ? (b) One-hundredth or 90 thousandths? (c) One-thousandth or 90 hundredths?
Answer
FirstSecondGreater
(a)10⁄1000 = 0.0101⁄10 = 0.1001⁄10
(b)one-hundredth = 0.01090 thousandths = 0.09090 thousandths
(c)one-thousandth = 0.00190 hundredths = 0.90090 hundredths
(a) 1⁄10 = 100⁄1000 and 100⁄1000 > 10⁄1000
(b) 1⁄100 = 10⁄1000 and 90⁄1000 > 10⁄1000
(c) 1⁄1000 = 0.001 and 90⁄100 = 0.9, which is 900 times bigger
Why it happens: the safest method is to rewrite both quantities with the same denominator (or the same number of decimal places) and then simply compare the numerators.
Q14.
Write the decimal forms of the quantities mentioned (an example is given): (a) 87 ones, 5 tenths and 60 hundredths = 88.10 (b) 12 tens and 12 tenths (c) 10 tens, 10 ones, 10 tenths, and 10 hundredths (d) 25 tens, 25 ones, 25 tenths, and 25 hundredths
Answer
WorkingDecimal form
(a)87 + 0.5 + 0.60 = 87 + 1.1088.10 (given)
(b)12 × 10 + 12 × 0.1 = 120 + 1.2121.2
(c)100 + 10 + 1.0 + 0.10111.1
(d)250 + 25 + 2.5 + 0.25277.75
Full working for (d):
25 tens = 25 × 10 = 250
25 ones = 25
25 tenths = 25 × 1⁄10 = 2.5
25 hundredths = 25 × 1⁄100 = 0.25
250 + 25 + 2.5 + 0.25 = 277.75
Why it happens: a place value can hold more than 9 of its own units in a description like this — "60 hundredths" is fine, and it simply regroups into 6 tenths, which then joins the 5 tenths to make 11 tenths, i.e. 1 unit and 1 tenth.
Tip: handle each phrase separately, write it as a decimal, and only then add the four numbers.
Q15.
Using each digit 0 – 9 not more than once, fill the boxes below so that the sum is closest to 10.5:
Answer

The boxes make two numbers of the form □.□□□ each, so eight different digits are used in all.

One exact solution:
  9.468
+ 1.032
= 10.500
Digits used: 9, 4, 6, 8, 1, 0, 3, 2 — all different ✓

Other exact solutions include:

First numberSecond numberSum
9.8570.64310.500
8.9761.52410.500
9.0321.46810.500
Why it happens: we need the thousandths digits to add to 10, the hundredths to 9 (plus the carry), the tenths to 4 (plus the carry) and the units to 10. Once the units are fixed at 9 + 1, plenty of choices remain for the three decimal places.
Tip: the book's answer key offers 9.476 + 1.025 = 10.501, which misses by 0.001. Since the sum can be made exactly 10.5, an exact pair such as 9.468 + 1.032 is the better answer.
Q16.
Write the following fractions in decimal form: (a) 1/2 (b) 3/2 (c) 1/4 (d) 3/4 (e) 1/5 (f) 4/5
Answer

Change each fraction into an equal fraction with denominator 10 or 100, then read off the decimal.

FractionMade into tenths / hundredthsDecimal
(a)1⁄21 × 5⁄2 × 5 = 5⁄100.5
(b)3⁄215⁄10 = 1 + 5⁄101.5
(c)1⁄41 × 25⁄4 × 25 = 25⁄1000.25
(d)3⁄475⁄1000.75
(e)1⁄51 × 2⁄5 × 2 = 2⁄100.2
(f)4⁄58⁄100.8
Why it happens: 2, 4 and 5 all divide exactly into 10 or 100, so each of these fractions can be rewritten with a power of ten below the line — and a fraction with denominator 10, 100 or 1000 is a decimal.
Did you know? Not every fraction behaves so well. 1⁄3 can never be written with a denominator of 10, 100 or 1000, so its decimal form 0.333… goes on forever. You will meet such decimals in higher classes.
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