Multiplication 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.

Rule

When a decimal number is multiplied by a power of ten, the product is found by moving the decimal point to the right that many places as the power of ten.

For example, in 3.45 10², the product is obtained by moving the decimal point two places to the right, i.e., 3.452 10² = 345.2

Problem 1

Multiply 4.569 10²

Solution

Step 1:

4.569 10²

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 4.569 is moved 2 places to the right and the product is obtained as shown below.

4.569 10² = 4.569 100 = 456.9

Problem 2

Multiply 17.3426 10³

Solution

Step 1:

17.3426 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 17.3426 is moved 3 places to the right and the product is obtained as shown below.

17.3426 10³ = 17.3426 1000 = 17342.6