Division of a Decimal by a Power of Ten

Definition

A power of ten is 10 raised to a whole number.

For example, 10¹ = 10; 10² = 100; 10³ = 1000 and so on.

A power of a ten has one followed by as many zeros as the power. For example, 10² is equal to one followed by two zeros, i.e., 100.

Formula

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

Problem 1

Divide 8.234 10²

Solution

Step 1:

8.234 10²

Here the power of ten is two or the number of zeros in its value 100 is 2.

Step 2:

So the decimal point in 8.234 is moved 2 places to the left and the quotient is obtained as shown below.

8.234 10² = 8.234 100 = 0.08234

Problem 2

Divide 14.76 10³

Solution

Step 1:

14.76 10³

Here the power of ten is three or the number of zeros in its value 1000 is 3.

Step 2:

So the decimal point in 14.76 is moved 3 places to the left and the quotient is obtained as shown below.

14.76 10³ = 14.76 1000 = 0.01476