Skill: Multiply by powers of 10

Multiplying by a power of $(10)$ moves every digit to a higher place-value position:

• $\times 10$: move each digit $1$ place left
• $\times 100$: move each digit $2$ places left
• $\times 1{,}000$: move each digit $3$ places left

The empty places are filled with zeros.

Example:

$$347 \times 100$$

Since $(100)$ has two zeros, move each digit in $(347)$ two places to the left:

• $3$ hundreds becomes $3$ ten-thousands.
• $4$ tens becomes $4$ thousands.
• $7$ ones becomes $7$ hundreds.

The ones and tens places are now empty, so zeros hold those places:

$$347 \times 100 = 34{,}700$$

So, multiplying by $(100)$ makes the number $(100)$ times as large by shifting its digits two place-value positions to the left.