# Multiplication of Decimal Numbers

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Reshma purchased 1.5kg vegetable at the rate of 8.50 rupees 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 decimals. Let us now learn the multiplication of two decimal numbers.

First we find 0.1 × 0.1.

Now, 0.1 =

Let us see it’s pictorial representation

The fraction

The shaded part in the picture represents

We know that,

To do this lets create another grid divided into 10 equal parts horizontally. Now move the second grid over the first grid to see how each 1/10th part of the first grid is divided into 10 equal parts or

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**Instructions:** Overlap one of the squares over the another and answer the questions.

How many small squares do you find in the above overlapped figure?

There are 100 small squares. The coloured square is one part out of 10 of the

How can we represent the square which has both the red and green colour?

So the **red and green coloured square** represents one out of 100 or 0.01. Hence, 0.1 × 0.1 =

**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.

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Let us now find 0.2 × 0.3.

We have, 0.2 × 0.3 =

As we did for

The intersected squares represent

Since there are 6 intersected squares out of 100, so they also reprsent 0.06. Thus, 0.2 × 0.3 =

Observe that 2 × 3 = 6 and the number of digits to the right of the decimal point in 0.06 is 2 (= 1 + 1).

Lets check whether this applies to 0.1 × 0.1 also. 0.1 x 0.1 =

1 x 1 = 1 and the number of digits to the right of the decimal point in 0.01 is 2 (= 1 + 1).

Lets 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 0.1 × 0.1 or 1 × 1.

Similarly in 0.2 × 0.3 we found 0.2 × 0.3 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.

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Let us now find 1.2 × 2.5.

Multiply

We get 300. Both, in 1.2 and 2.5, there is

So, count 1 + 1 = 2 digits from the rightmost digit (i.e.,

We get 3.00 or

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 =

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## Example 3

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

We have found the answer.

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## Example 4

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

We have found the answer.

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## Multiplication of Decimal Numbers by 10, 100 and 1000

Let us see if we can find a pattern of multiplying numbers by 10 or 100 or 1000. Have a look at the table given below and fill in the blanks:

Size (in inches) | Size (in inches) |
---|---|

1.76 x10= | 2.35 x10= |

1.76 x100= | 2.35 x100= |

1.76 x1000= | 2.35 x1000= |

Observe the shift of the decimal point of the products in the table. Here the numbers are multiplied by 10,100 and 1000. In 1.76 × 10 =

Note that 100 has two zeros over one.

So we say, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.

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Answer the below questions