NCERT Solutions Ganita Prakash (Part 1) Chapter 3 In-text Questions — A Tenth Part

Book page 52 Updated on2026-09-05

Q1.

Try computing the difference by converting both lengths to tenths.

Answer

Change 12 ⁴⁄₁₀ and 6 ⁷⁄₁₀ into tenths first.

12 ⁴⁄₁₀ = ¹²⁰⁄₁₀ + ⁴⁄₁₀ = ¹²⁴⁄₁₀
6 ⁷⁄₁₀ = ⁶⁰⁄₁₀ + ⁷⁄₁₀ = ⁶⁷⁄₁₀
¹²⁴⁄₁₀ – ⁶⁷⁄₁₀ = ^{124 – 67}⁄₁₀ = ⁵⁷⁄₁₀
= ⁵⁰⁄₁₀ + ⁷⁄₁₀ = 5 ⁷⁄₁₀ units

Why it happens: once both numbers use the same unit (one-tenth), subtracting them is an ordinary whole-number subtraction, 124 – 67 = 57. The denominator just tags along.

Tip: this method needs no borrowing between "units" and "tenths" — all the borrowing happens inside the plain subtraction 124 – 67.

Q2.

A Celestial Pearl Danio’s length is 2 4/10 cm, and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?

Answer

2 ⁴⁄₁₀ – ⁹⁄₁₀
= ²⁴⁄₁₀ – ⁹⁄₁₀
= ¹⁵⁄₁₀
= ¹⁰⁄₁₀ + ⁵⁄₁₀
= 1 ⁵⁄₁₀ cm (that is, 1.5 cm)

Why it happens: 9 tenths cannot be taken from 4 tenths, so one whole unit of the Danio's length is opened into 10 tenths: 2 ⁴⁄₁₀ becomes 1 unit and 14 tenths. Then 14 – 9 = 5 tenths, leaving 1 ⁵⁄₁₀ cm.

Did you know? The Philippine Goby, at about ⁹⁄₁₀ cm, is one of the smallest fish in the world — shorter than the width of your little fingernail.

Q3.

How big are these fish compared to your finger?

Answer

Measure your own index finger with a ruler and compare. A Class 7 student's index finger is usually about 6 to 7 cm long.

Fish	Length	Compared with a 6 cm finger
Celestial Pearl Danio	2 ⁴⁄₁₀ cm	about ²⁄₅ of the finger — a little less than half
Philippine Goby	⁹⁄₁₀ cm	less than ¹⁄₆ of the finger — about the width of a fingernail

Check it yourself: mark 2 ⁴⁄₁₀ cm and ⁹⁄₁₀ cm on a strip of paper and hold it against your finger. Write down the comparison for your finger — the answer will be different for everyone.

Q4.

Observe the given sequences of numbers. Identify the change after each term and extend the pattern: (a) 4, 4 3/10, 4 6/10, ___ (b) 8 2/10, 8 7/10, 9 2/10, ___ (c) 7 6/10, 8 7/10, ___ (d) 5 7/10, 5 3/10, ___ (e) 13 5/10, 13, 12 5/10, ___ (f) 11 5/10, 10 4/10, 9 3/10, ___

Answer

Find the change from one term to the next, then keep applying it four more times.

	Change	Next four terms
(a) 4, 4 ³⁄₁₀, 4 ⁶⁄₁₀	add ³⁄₁₀	4 ⁹⁄₁₀, 5 ²⁄₁₀, 5 ⁵⁄₁₀, 5 ⁸⁄₁₀
(b) 8 ²⁄₁₀, 8 ⁷⁄₁₀, 9 ²⁄₁₀	add ⁵⁄₁₀	9 ⁷⁄₁₀, 10 ²⁄₁₀, 10 ⁷⁄₁₀, 11 ²⁄₁₀
(c) 7 ⁶⁄₁₀, 8 ⁷⁄₁₀	add 1 ¹⁄₁₀	9 ⁸⁄₁₀, 10 ⁹⁄₁₀, 12, 13 ¹⁄₁₀
(d) 5 ⁷⁄₁₀, 5 ³⁄₁₀	subtract ⁴⁄₁₀	4 ⁹⁄₁₀, 4 ⁵⁄₁₀, 4 ¹⁄₁₀, 3 ⁷⁄₁₀
(e) 13 ⁵⁄₁₀, 13, 12 ⁵⁄₁₀	subtract ⁵⁄₁₀	12, 11 ⁵⁄₁₀, 11, 10 ⁵⁄₁₀
(f) 11 ⁵⁄₁₀, 10 ⁴⁄₁₀, 9 ³⁄₁₀	subtract 1 ¹⁄₁₀	8 ²⁄₁₀, 7 ¹⁄₁₀, 6, 4 ⁹⁄₁₀

Why it happens: the easiest way to run each pattern is to work in tenths. For (c), 76, 87, 98, 109, 120, 131 tenths — the numerator simply goes up by 11 each time, and ¹²⁰⁄₁₀ is the whole number 12.

Tip: when the tenths reach 10, exchange them for one unit. In (f), 6 ¹⁄₁₀ – 1 ¹⁄₁₀ would come after 6, but the term before 6 is 7 ¹⁄₁₀, so the next term is exactly 6, and then 4 ⁹⁄₁₀.

Q5.

The length of a sheet of paper was 8 9/10 units, which can also be said as 8 units and 9 one-tenths. It is folded in half along its length. What is its length now?

Answer

Folding in half means taking half of 8 ⁹⁄₁₀.

8 ⁹⁄₁₀ = ⁸⁹⁄₁₀ units
Half of ⁸⁹⁄₁₀ = ⁸⁹⁄₂₀ = ^44.5⁄₁₀
= 4 units + 4 tenths + half a tenth
= 4 ⁴⁄₁₀ ⁵⁄₁₀₀ units

Why it happens: half of 8 units is 4 units; half of 9 tenths is 4 tenths and half a tenth left over. A tenth-scale has no mark for half a tenth, so on that scale we can only say the folded length lies between 4 ⁴⁄₁₀ and 4 ⁵⁄₁₀. Splitting each tenth into 10 equal parts gives one-hundredths, and half a tenth is exactly ⁵⁄₁₀₀.

Tip: this is exactly why the book moves on to hundredths in Section 3.3 — tenths were not fine enough for this fold.

Was this helpful? Report an error