Powers of Ten

When multiplying like bases, keep the base and add exponents. When finding the value of ten to a power, 10 ⁿ, use 10 as a factor ‘n’ times. When dividing like bases, keep the base and subtract exponents.

Example:

10 ² x 10 ³ = 10 ²⁺³ = 10 ⁵ = 10 x 10 x 10 x 10 x 10 = 100000.

10 ⁶ ÷ 10 ³ = 10 ^6-3 = 10 ³ = 10 x 10 x 10 = 1000

Multiplication and Division by powers of ten

A power of ten is a number that can be written as a product of tens; 10, 100, 1000, 10,000 are powers of ten. In exponential form, these are 10 ¹, 10 ², 10 ³, and 10 ⁴. A power of ten can be recognized by looking for the number 10 written with an exponent or a single ‘1’ followed by zeros.

To multiply a number by a power of ten, move the decimal point to the right.

To divide a number by a power of ten, move the decimal point to the left. The number of places to move, either left or right, is shown by the number of zeros in the power of ten. Zeros may have to be placed to the right or the left of the number in order to move the correct number of decimal places.

Examples

Multiply: 5.6(10,000)

10,000 has 4 zeros; therefore, 3 zeros have to be placed to the right of the number, ‘5.6’, in order to move the correct number of decimal places.

5.6(10,000) = 56,000

Divide: 5.6 ÷ 10,000

3 zeros have to be placed to the left of the number, ‘5.6’, in order to move the correct number of decimal places.

5.6 ÷ 10,000 = .00056 3.828 x 100 = 382.8 382.8 ÷1000 = .3828