Multiply by powers of 10

Multiplying a whole number by a power of 10 scales it by place-value units: multiplying by 10, 100, or 1,000 moves each digit one, two, or three places to the left, respectively. The resulting zeros are understood as placeholders created when digits occupy higher place-value positions, rather than as a rule to append zeros without regard to the number’s structure. This understanding supports efficient computation and later work with place value and powers of 10; generalized exponent rules and arbitrary decimal scaling are not included here.

Detailed Explanation: 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.

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Multiplication - Tens, Hundreds, Thousands - Columns

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Multiply by powers of 10

Detailed Explanation: Multiply by powers of 10

Learn by doing: Multiply by powers of 10

Practice with unlimited practice problems

Practice:

Multiplication - Tens, Hundreds, Thousands - Columns