Skill: Divide decimals by powers of ten

Dividing by a power of ten makes the number smaller:

• Divide by $(10)$: each digit shifts 1 place to the right.
• Divide by $(100)$: each digit shifts 2 places to the right.
• Divide by $(1{,}000)$: each digit shifts 3 places to the right.

Zeros may be needed as placeholders.

Example: $(6.3 \div 1{,}000)$

Since $(1{,}000)$ has three zeros, shift each digit three places to the right:

$$6.3 \div 10=0.63$$ $$6.3 \div 100=0.063$$ $$6.3 \div 1{,}000=0.0063$$

So,

$$\boxed{6.3\div 1{,}000=0.0063}$$

The zeros in $(0.0063)$ are placeholders. They show that the $6$ is now in the thousandths place. The decimal point is written in its new place after the digits have shifted; it does not move by itself.