Multiply decimals by powers of ten

Multiplying a decimal by a positive integral power of ten increases each digit’s place value by the corresponding number of places: multiplying by 10, 100, or 1,000 makes the number 10, 100, or 1,000 times as large, respectively. Place-value charts and equivalent decimal representations clarify that the digits retain their relationships while the decimal point is repositioned, with zeros added when needed; this scope does not include negative powers, arbitrary exponents, or scientific notation.

Detailed Explanation: Multiply decimals by powers of ten

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

Multiply by $10$ : move it $1$ place.
Multiply by $100$ : move it $2$ places.
Multiply by $1{,}000$ : move it $3$ places.

Each place to the right makes the number $10$ times larger. Add zeros if the decimal point moves past the last digit.

Example

Find $4.56 \times 1{,}000$ .

Since $1{,}000$ has three zeros, move the decimal point $3$ places to the right:

4.56 \rightarrow 45.6 \rightarrow 456. \rightarrow 4560.

Therefore,

4.56 \times 1{,}000 = 4{,}560.

The zero is added because there were not enough digits after the decimal point to move it three places.

Learn by doing: Multiply decimals by powers of ten

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Multiplication - Decimal by Power of Ten (Scientific Notation Prep)

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