NCERT Book Class 6 Maths Decimals

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Decimals

8.1 Introduction

Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. 

They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”.

Have they written correctly?

We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals.

8.2 Tenths

Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals?

We know that 10 mm = 1 cm

Therefore, 1 mm         =1 /10 cm or one-tenth cm = 0.1 cm

Now, length of Ravi’s pencil = 7cm 5mm

                                        = 75/10 cm i.e. 7cm and 5 tenths of a cm

                                        = 7.5cm

The length of Raju’s pencil = 8 cm 3 mm = 83 /10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm

Let us recall what we have learnt earlier.

If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1 10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on. A combination of 2 blocks and 3 parts (tenths) will be recorded as :

Ones            Tenths

(1)                 (1 /10 )

2                   3

It can be written as 2.3 and read as two point three.

Let us look at another example where we have more than ‘ones’. Each tower represents 10 units. So, the number shown here is :

Representing Decimals on number line

We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line. We know that 0.6 is more than zero but less than one. There are 6 tenths in

it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below :

Write five numbers between 0 and 1 and show them on the number line.

Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line? Show 1.4 on the number line.

Example 1 : Write the following numbers in the place value table :

(a) 20.5     (b) 4.2

Solution : Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have, 

Fractions as decimals 

We have already seen how a fraction with denominator 10 can be represented using decimals.

Let us now try to find decimal representation of

(a)11 / 5       (b)1 / 2

(a) We know that

11 / 5 = 22 / 10 = 20 +2/ 10 = 20 / 10 + 2 / 10 = 2 + 2 / 10 = 2.2

Therefore, 22 / 10 = 2.2 (in decimal notation.)

Please refer to attached file for NCERT Class 6 Maths Decimals