Arithmetic : Decimals

Multiplication of Decimals

To multiply decimals,

• multiply the numbers in the same way as whole numbers (ignoring the decimal point); and
• insert a decimal point in the result such that the decimal places in the product equal the sum total of the decimal places in all the numbers multiplied.

For example to multiply 1.01, 0.3 and 0.002, the whole numbers are first multiplied to obtain 101 × 3 × 2 = 606. There are two decimal places in 1.01, one decimal place in 0.3 and 3 decimal places in 0.002. So, the product must have 2 + 1 + 3 = 6 decimal places. Thus, 1.01 × 0.3 × 0.002 = 0.000606

Example
Sharon buys apples costing $0.23 each. How much should she pay for 9 apples?
Solution. To multiply 0.23 × 9, the whole numbers are first multiplied to obtain 23 × 9 = 207. Since there are two decimal places in 0.23 and zero decimal places in 9, the product must have 2 + 0 = 2 decimal places. Thus, 0.23 × 9 = 2.07. So, Sharon should pay $2.07 for 9 apples.

MUST-KNOW : When a decimal is multiplied by 10, 100, 1000, ..., the decimal point moves to the right by 1, 2, 3, ... places.

For example, 54.1266 × 10 = 541.266, 54.1266 × 100 = 5412.66, 54.1266 × 1000 = 54126.6