NCERT Solutions For Class 6 Maths Chapter 8 Exercise 8.6
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 × 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 × 0.1.
Now, 0.1 =
1
10 . So, 0.1 × 0.1 =
1 1
×
10 10
=
1×1
10×10
=
1
100
= 0.01.
Let us see it’s 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
×
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
×
10 10 or 0.1 × 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 × 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 × 0.3.
We have, 0.2 × 0.3 =
2 3
×
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
×
10 10 .
The dotted squares represent
2 3
×
10 10 or 0.2 × 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 × 0.3 = 0.06.
Observe that 2 × 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 × 0.1 also.
Find 0.2 × 0.4 by applying these observations.
While finding 0.1 × 0.1 and 0.2 × 0.3, you might have noticed that first we
multiplied them as whole numbers ignoring the decimal point. In 0.1 × 0.1, we found
01 × 01 or 1 × 1. Similarly in 0.2 × 0.3 we found 02 × 03 or 2 × 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 × 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 × 1.6, 2.4 × 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 × 1.25 = 3.225
Find 2.7 × 1.35.
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