## Ncert Solutions for Class 6 Maths Chapter 8 Decimals Exercise 8.6:-

**Exercise 8.6**Class 6 maths NCERT solutions Chapter 8 Decimals pdf download:-

### Ncert Solution for Class 6 Maths Chapter 8 Decimals Exercise 8.6 Tips:-

**MULTIPLICATION OF DECIMAL NUMBERS**

Reshma purchased 1.5kg vegetable at the rate of ` 8.50 per kg. How much money should

she pay? Certainly it would be ` (8.50 Ć 1.50). Both 8.5 and 1.5 are decimal numbers.

So, we have come across a situation where we need to know how to multiply two deci-

mals. Let us now learn the multiplication of two decimal numbers.

First we find 0.1 Ć 0.1.

Now, 0.1 =

1

10 . So, 0.1 Ć 0.1 =

1 1

Ć

10 10

=

1Ć1

10Ć10

=

1

100

= 0.01.

Let us see itās pictorial representation (Fig 2.13)

The fraction

1

10 represents 1 part out of 10 equal parts.

The shaded part in the picture represents

1

10 .

We know that,

1 1

Ć

10 10 means

1

10 of

1

10 . So, divide this

1

10 th

part into 10 equal parts and take one part

out of it. Fig 2.13

FRACTIONS AND DECIMALS 49

Thus, we have, (Fig 2.14).

Fig 2.14

The dotted square is one part out of 10 of the

1

10 th

part. That is, it represents

1 1

Ć

10 10 or 0.1 Ć 0.1.

Can the dotted square be represented in some other way?

How many small squares do you find in Fig 2.14?

There are 100 small squares. So the dotted square represents one out of 100 or 0.01.

Hence, 0.1 Ć 0.1 = 0.01.

Note that 0.1 occurs two times in the product. In 0.1 there is one digit to the right of

the decimal point. In 0.01 there are two digits (i.e., 1 + 1) to the right of the decimal point.

Let us now find 0.2 Ć 0.3.

We have, 0.2 Ć 0.3 =

2 3

Ć

10 10

As we did for

1

10

1

10 , let us divide the square into 10

equal parts and take three parts out of it, to get

3

10 . Again

divide each of these three equal parts into 10 equal parts and

take two from each. We get 2 3

Ć

10 10 .

The dotted squares represent

2 3

Ć

10 10 or 0.2 Ć 0.3. (Fig 2.15)

Since there are 6 dotted squares out of 100, so they also

reprsent 0.06. Fig 2.15

50 MATHEMATICS

Thus, 0.2 Ć 0.3 = 0.06.

Observe that 2 Ć 3 = 6 and the number of digits to the right of the decimal point in

0.06 is 2 (= 1 + 1).

Check whether this applies to 0.1 Ć 0.1 also.

Find 0.2 Ć 0.4 by applying these observations.

While finding 0.1 Ć 0.1 and 0.2 Ć 0.3, you might have noticed that first we

multiplied them as whole numbers ignoring the decimal point. In 0.1 Ć 0.1, we found

01 Ć 01 or 1 Ć 1. Similarly in 0.2 Ć 0.3 we found 02 Ć 03 or 2 Ć 3.

Then, we counted the number of digits starting from the rightmost digit and moved

towards left. We then put the decimal point there. The number of digits to be counted

is obtained by adding the number of digits to the right of the decimal point in the

decimal numbers that are being multiplied.

Let us now find 1.2 Ć 2.5.

Multiply 12 and 25. We get 300. Both, in 1.2 and 2.5, there is 1 digit to the right

of the decimal point. So, count 1 + 1 = 2 digits from the rightmost digit (i.e., 0) in 300

and move towards left. We get 3.00 or 3.

Find in a similar way 1.5 Ć 1.6, 2.4 Ć 4.2.

While multiplying 2.5 and 1.25, you will first multiply 25 and 125. For placing the

decimal in the product obtained, you will count 1 + 2 = 3 (Why?) digits starting from

the rightmost digit. Thus, 2.5 Ć 1.25 = 3.225

Find 2.7 Ć 1.35.