# 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