NCERT Solutions Ganita Prakash (Part 1) Chapter 3 –47Section 3.1 The Need for Smaller Units — In-text Questions

Book page 46 Updated on2026-09-05

Q1.

In the following figure, screws are placed above a scale. Measure them and write their length in the space provided.

Answer

The same screw is shown three times, above three different scales. The screw on the left is 2 ⁷⁄₁₀ cm long and the screw on the right is 3 ²⁄₁₀ cm long. What you can write depends on how finely the scale is marked.

Scale used	Left screw (given)	Right screw (to fill)
Only whole centimetres marked	Between 2 cm and 3 cm	Between 3 cm and 4 cm
Half centimetres marked	More than 2 ¹⁄₂ cm but less than 3 cm	More than 3 cm but less than 3 ¹⁄₂ cm
Tenths of a centimetre marked	2 ⁷⁄₁₀ cm	3 ²⁄₁₀ cm

Why it happens: the tip of the right-hand screw falls 2 small divisions past the 3 cm mark. On the finest scale each small division is ¹⁄₁₀ cm, so the reading is 3 cm and 2 tenths — that is, 3 ²⁄₁₀ cm.

Tip: the difference between the two screws is 3 ²⁄₁₀ – 2 ⁷⁄₁₀ = ⁵⁄₁₀ cm, i.e. only half a centimetre. That tiny gap was enough to stop Sonu's mother from fixing the toy.

Q2.

Which scale helped you measure the length of the screws accurately? Why?

Answer

The third scale — the one in which each centimetre is divided into 10 equal parts.

Why it happens: the tip of the screw does not land on a whole-centimetre mark. On the first scale we can only say "between 2 cm and 3 cm". The second scale, with half-centimetre marks, narrows it to "more than 2 ¹⁄₂ cm but less than 3 cm". Only the third scale has a mark exactly where the tip is, so it gives the exact length 2 ⁷⁄₁₀ cm.

Tip: the smaller the unit on the scale, the more accurate the measurement. That is the whole idea behind this chapter.

Q3.

What is the meaning of 2 7/10 cm (the length of the first screw)?

Answer

It means 2 whole centimetres and 7 one-tenths of a centimetre.

On the ruler, the length between two consecutive numbers is cut into 10 equal parts.
Each part = ¹⁄₁₀ cm
Go from 0 to 2 → 2 cm
Then take 7 more parts → 7 × ¹⁄₁₀ = ⁷⁄₁₀ cm
Total = 2 cm + ⁷⁄₁₀ cm

Why it happens: a mixed number like 2 ⁷⁄₁₀ is just "2 units plus 7 of the small parts". The same length can also be written as 27 one-tenths, because 2 cm itself is 20 one-tenths: ²⁰⁄₁₀ + ⁷⁄₁₀ = ²⁷⁄₁₀.

Read it as: "two and seven-tenth centimeters". Similarly 3 ²⁄₁₀ cm is read "three and two-tenth centimeters".

Q4.

Can you explain why the unit was divided into smaller parts to measure the screws?

Answer

Because the screws did not end exactly at a centimetre mark.

Why it happens: a measuring unit can only report lengths that are whole multiples of itself. With centimetres alone, both screws would be reported as "about 3 cm" and would look identical — yet one was 2 ⁷⁄₁₀ cm and the other 3 ²⁄₁₀ cm. Cutting the centimetre into 10 equal parts gives a smaller unit (¹⁄₁₀ cm = 1 mm), and now the two screws get different, exact readings.

Did you know? The very same trouble made Sonu's mother's toy refuse to hold together. In machines, a ⁵⁄₁₀ cm error in a screw can be the difference between a working part and a broken one.

Q5.

Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.

Answer

This is a hands-on activity — do it with your own ruler. Line up the left end of the object with the 0 mark (not with the edge of the ruler), then read off the mark at the other end.

Object	Sample reading	In tenths	Read as
Pen	13 ⁵⁄₁₀ cm	¹³⁵⁄₁₀ cm	thirteen and five-tenth centimeters
Sharpener	2 ⁴⁄₁₀ cm	²⁴⁄₁₀ cm	two and four-tenth centimeters
Eraser	3 ⁸⁄₁₀ cm	³⁸⁄₁₀ cm	three and eight-tenth centimeters

Check it yourself: your own pen will not give exactly 13 ⁵⁄₁₀ cm — write down whatever your ruler shows. Always give the answer in the form "whole centimetres + tenths".

Q6.

Write the measurements of the objects shown in the picture:

Answer

Each object is drawn with its left end at 0, so read the mark at the right end.

Object	Length	Same length in tenths	Read as
Eraser	2 ⁴⁄₁₀ cm	²⁴⁄₁₀ cm	two and four-tenth centimeters
Pencil	4 ⁵⁄₁₀ cm	⁴⁵⁄₁₀ cm	four and five-tenth centimeters
Piece of chalk	1 ⁴⁄₁₀ cm	¹⁴⁄₁₀ cm	one and four-tenth centimeters

Why it happens: the pencil ends exactly halfway between 4 cm and 5 cm. Five tenths is half of ten tenths, so 4 ⁵⁄₁₀ cm is the same as 4 ¹⁄₂ cm.

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