# 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