Multiplication of Decimal Numbers

• Decimal multiplication through models

Notes

Multiplication of Decimal Numbers:

Let us now learn the multiplication of two decimal numbers.

1) Find 0.1 × 0.1.

Now, 0.1 = 1/10. "So", 0.1 xx 0.1 = 1/10 xx 1/10 = (1xx1)/(10xx10) = 1/100 = 0.01.

Let us see it’s a pictorial representation,

The fraction 1/10 represents 1 part out of 10 equal parts. The shaded part in the picture represents 1/10.
We know that, 1/10 xx 1/10 "means" 1/10 "of" 1/10.

So, divide this 1/10th part into 10 equal parts and take one part out of it.

Thus, we have,

The dotted square is one part out of 10 of the 1/10th part. That is, it represents 1/10 xx 1/10 "or"  0.1 xx 0.1.

There are 100 small squares. So the dotted square represents one out of 100 or 0.01. Hence, 0.1 × 0.1 = 0.01.

2) Find 0.2 × 0.3.

We have, 0.2 × 0.3 = 2/10 xx 3/10

As we did for 1/10 xx 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 2/10 xx 3/10.

The dotted squares represent 2/10 xx 3/10 or 0.2 × 0.3.

Since there are 6 dotted squares out of 100, so they also represent 0.06.

Thus, 0.2 × 0.3 = 0.06.

Example

Multiply 0.1 × 0.1

 0.1 × 0.1 0 1 + 0 0 0 0 . 0 1

Example

Multiply 2.3 × 3.8

 2.3 × 3.8 184 + 690 8.74

Example

Multiply 1.25 × 3.78

 1.25 × 3.78 1000 + 8750 + 37500 4.725

Example

The side of an equilateral triangle is 3.5 cm. Find its perimeter.

All the sides of an equilateral triangle are equal.

So, length of each side = 3.5 cm

Thus, perimeter = 3 × 3.5 cm = 10.5 cm

Example

The length of a rectangle is 7.1 cm and its breadth is 2.5 cm. What is the area of the rectangle?

Length of the rectangle = 7.1 cm

Breadth of the rectangle = 2.5 cm

Therefore, area of the rectangle = 7.1 × 2.5 cm2 = 17.75 cm2

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Multiplication of Decimal Numbers [00:17:34]
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