Powers of 10 can be written in two ways:
• With an exponent: 10³
• In expanded form: 1000 (1000 = 10³, note that the number of zeros is equivalent to the exponent)
Multiplying by a positive power of 10 makes the number larger and multiplying by a negative power of 10 makes the number smaller.
5 x 10¹= 5 x 10 = 50
5 x 10²= 5 x 100 = 500
5 x 10³= 5 x 1,000 = 5,000
5 x 10⁴= 5 x 10,000 = 50,000
To multiply a whole number by a power of ten, just count how many zero you have and attach that to the whole number.
To divide by a power of 10, simply move the decimal point to the left the same number of places as the exponent or as the number of zeros. Example:
50 / 10¹= 50/10 = 5
500/10² = 500/100 = 5
5000/10³ = 5000/1000 = 5
Note: The decimal point of a whole number is always to the right of the one’s place.
Positive, negative and zero exponents with a base of ten
When we multiply a number by a positive power of 10, we move the decimal point of the number to the right.
When we multiply a number by a negative power of 10, we move the decimal point of the number to the left.
The number of places to move would be equal to the power of ten.