# Multiplication of a Decimal by a Power of 0.1

A power of 0.1 is 10 raised to a negative whole number as follows

0.1 = 10−1; (0.1)2 = 10−2 = 0.01; (0.1)3 = 10−3 = 0.001 and so on.

A power of a 0.1 has one preceded by zeros with as many decimal places as the power of 0.1.
For example, (0.1)2 is equal to 0.01 which has as many decimal places (2) as the power of 0.1 which is 2.

Rules

The product of a decimal multiplied by a power of 0.1 can be found by a short cut. When a decimal number is multiplied by a power of 0.1, the product is found by moving the decimal point to the left that many places as the power of 0.1

Multiply 27.43 × (0.1)2

### Solution

27.43 × (0.1)2

Here the power of 0.1 is two and there are two decimal places in its value 0.01. So the decimal point in 27.43 is moved 2 places to the left and the product is obtained as shown below.

27.43 × (0.1)2 = 27.43 × 0.01 = 0.2743

Multiply 16.26 × (0.1)3

### Solution

16.26 × (0.1)3

Here the power of 0.1 is three and the number of decimal places in its value 0.001 is 3. So the decimal point in 16.26 is moved 3 places to the left and the product is obtained as shown below. A zero is added before 1 to make three places shift to the left.

16.26 × (0.1)3 = 16.26 × 0.001 = 0.01626