Dividing decimals by powers of ten means using exponents to understand how a number changes when it is divided by 10, 100, 1,000, or other powers of ten. A power of ten is any number that can be written as 10n, where n is the exponent.
The exponent tells you how many zeros the power of ten has.
When you divide a decimal by a power of ten, the digits in the number move to the right. Each place-value shift is controlled by the exponent.
Dividing by 10n always shifts the digits n places right, not the decimal point.
We use exponents to write powers of ten in a shorter way. This helps us describe how much a number will change when it is divided.
Think of the exponent as a “shift counter” that tells you how far the digits move.
The same rules work whether the number is a whole number, a decimal, or a mixed decimal. Dividing by powers of ten always reduces the value by shifting digits right.
If zeros appear in front of the number, that is normal. They show the place-value shift correctly.
Place-value reasoning helps explain why digits shift. Each division by 10 reduces a digit’s value to one-tenth of what it was before.
Dividing never changes the order of digits—only their place values.
Patterns in the number help confirm your answer. The quotient should always be smaller when you divide by a power of ten.
If your quotient becomes larger, check your place-value shifts again.