Skill: 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 $4.56 \times 1{,}000$.

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

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

2. 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.