MULTIPLICATION OF DECIMALS

Lily purchased 2.5 lbs fruits at the rate of $3.50 per lb. How much money should she pay?

Certainly it would be $(2.5 x 3.50). Both 2.5 and 3.5 are decimal numbers.

Now, we have come across a situation where we need to know how to multiply two decimals. So we now learn the multiplication of two decimal numbers.

Now, let us find 1.5 x 4.3.

Multiplying 15 and 43, we get 645.

Both, in 1.5 and 4.3, there is 1 digit to the right of the decimal point. So, count 2 digits from the right and put a decimal point.

So, we get 1.5 x 4.3 = 6.45. 

While multiplying 1.43 and 2.1, you will first multiply 143 and 21. For placing the decimal in the product obtained, you will count 2 + 1 = 3 digits starting from the right most digit.

Thus 1.43 × 2.1 = 3.003.

Lily observed that

3.7 = 37/10

3.72 = 372/100

3.723 = 23723/1000

Thus, she found that depending on the position of the decimal point the decimal number can be converted to a fraction with denominator 10 , 100 or 1000.

Now let us see what would happen if a decimal number is multiplied by 10 or 100 or 1000.

For example,

3.23 x 10 = (323/100) x 10 = 323/10 = 32.3

Decimal point shifted to the right by one place since 10 has one zero.

3.23 x 100 = (323/100) x 100 = 32.3

Decimal point shifted to the right by one place since 100 has two zeros.

3.23 x 1000 = (323/100) x 1000 = 323 x 10 = 3230

Decimal point shifted to the right by one place since 1000 has three zeros.

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