## Multiplying Decimals

Multiplying decimals is similar to multiplying whole numbers except for the placement of the decimal points.

## Multiplying Decimals with Whole Numbers

Consider the product 3 × 1.5.

This is equivalent to adding the decimal number 1.5 three times.

That is, 1.5 + 1.5 + 1.5 = 4.5.

The fraction-equivalent of the decimal 1.5 is 1510. So, adding them thrice gives us:

^{15}⁄_{10}+ ^{15}⁄_{10 }+ ^{15}⁄_{10 }= ^{15+15+15}⁄_{10 }= ^{45}⁄_{10 }= 4.5

The first step in the standard procedure for multiplying a decimal and a whole number is multiplying the two numbers as two whole numbers. After that, count the number of places equivalent to that of the decimal places in the factor and put the decimal point.

Here, to find 3 × 1.5, first multiply the two numbers as whole numbers.

3 × 15 = 45

Now, the decimal in the factors, 1.5 has only one digit after the decimal point. So, the product also will have the same. Therefore, mark the decimal point between 4 a 5.

3 × 1.5 = 4.5

When you multiply any decimal by 10, 100, or 1000, the decimal point move 1, 2, or 3 places to the left respectively.

**For example**:

This applies when you multiply by multiples of 10.

**For example**:

50 × 2.5 = 5 × 10 × 2.5 = 5 × 25 = 125

## Multiplying Two Decimal Numbers

Consider the product 3.6 × 1.3. Here, it is difficult to find the product using multiplication as repeated addition. The easiest way is to find the product is by following the standard procedure.

Step 1: Multiply the two numbers as two whole numbers.

Thus, 36 × 13 = 468.

Step 2: Now, there is one digit each after the decimal point in the factors. So, the product will have 1 + 1 = 2 digits after the decimal point.

Therefore, 3.6 × 1.3 = 4.68.

Factor 3.6 can be approximated to 4 and 1.3 to 1. So, their product can be estimated to be 4. This will help you in verifying the placement of the decimal point.

The fraction-equivalents of the products are 3610 and 1310.

Taking the products: ^{36}⁄_{10 }x ^{13}⁄_{10 }= ^{36×13}⁄_{10×10 }= ^{468}⁄_{100 }= 4.68

Fun fact:1. The word decimal originated from the Latin word ‘decimus’ which means one-tenth. 2. The first place after the decimal point is of tenth, the second place is one-tenth of one-tenth that is one-hundredth, the third is one-thousandth etc. |