Divide decimals by powers of ten

Dividing a decimal by 10, 100, or 1,000 means finding one-tenth, one-hundredth, or one-thousandth of its value, so each digit shifts one, two, or three places to the right in the place-value system. The quotient may require zeros as placeholders, and the decimal point does not “move” independently of the digits; this understanding supports decimal multiplication, measurement conversions, and later work with powers of ten.

Detailed Explanation: 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.

Learn by doing: Divide decimals by powers of ten

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Division by Powers of Ten (Positive)

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