Divide by powers of 10

Dividing a whole number by 10, 100, or 1,000 is understood as partitioning by one, two, or three factors of ten: each place-value unit becomes ten times smaller, represented by shifting digits to the right in a place-value chart. Quotients may be whole numbers or terminating decimals, and zeros act as placeholders; removing zeros is valid only when the dividend has corresponding trailing zeros. The focus is base-ten place-value reasoning, not arbitrary exponents or generalized algebraic rules.

Detailed Explanation: Divide by powers of 10

To divide a whole number by $10$ , $100$ , or $1{,}000$ , move each digit to a place that is respectively one, two, or three places to the right in a place-value chart. Each move makes the value of a digit $10$ times smaller.

Example: $37 \div 100$

Since $100$ has two factors of $10$ ,

100=10\times10,

move the digits two places to the right:

Start with $37$ :
- $3$ is in the tens place.
- $7$ is in the ones place.
Divide by $10$ once:
$3$ moves to the ones place, and $7$ moves to the tenths place.

37\div10=3.7

Divide by $10$ one more time:
$3$ moves to the tenths place, and $7$ moves to the hundredths place.

37\div100=0.37

The $0$ before the decimal is a placeholder showing that there are no whole ones. Therefore,

\boxed{37\div100=0.37}

Removing zeros works only when the dividend has matching trailing zeros. For example, $4{,}800\div100=48$ because two zeros can be removed.

Learn by doing: Divide by powers of 10

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Division by Powers of Ten (Positive)

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