# Division 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.

Formula

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

Divide 36.193 ÷ (0.1)2

### Solution

Step 1:

36.193 ÷ (0.1)2

Here the power of 0.1 is two or there are two decimal places in its value 0.01.

Step 2:

So the decimal point in 36.193 is moved 2 places to the right and the quotient is obtained as shown below.

36.193 ÷ (0.1)2 = 36.193 ÷ 0.01 = 3619.3

Divide 41.15 ÷ (0.1)3

### Solution

Step 1:

41.15 ÷ (0.1)3

Here the power of 0.1 is three or the number of decimal places in its value 0.001 is 3.

Step 2:

So the decimal point in 45.15 is moved 3 places to the right and the quotient is obtained as shown below. A zero is added after 1 to make three places shift to the right.

41.15 ÷ (0.1)3 = 41.15 ÷ 0.001 = 41150