In any multiplication problem, the numbers being multiplied are called the
factors.
For example, in the multiplication problem
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$\,23.7\times 10\,$,
the factors are
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$\,23.7\,$ and $\,10\,$.
To multiply a decimal by powers of ten,
you move the decimal point one place
to the right for each factor of ten.
Recall that $\,10^5\,$ is a shorthand for $\,5\,$ factors of $\,10\,$: $\,10^5 = 10\cdot 10\cdot 10\cdot 10\cdot 10\,$.
Similarly, $\,10^n\,$ is a shorthand for $\,n\,$ factors of $\,10\,$.
The
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$\,\times\,$ symbol is used
for multiplication in these problems, because the centered dot is too easily confused with
the decimal point.
To divide a decimal by powers of ten, you move the decimal point one place to the left for each factor of ten.
In this web exercise, division is denoted using either the ‘[beautiful math coming... please be patient] $\,\div\,$’ symbol, or a horizontal fraction bar.
Make sure you understand why this works!
For example, when
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$\,2.37\,$ is divided by $\,10\,$, the
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$\,2\,$ ones should turn into $\,2\,$ tenths.
Moving the decimal point one place to the left accomplishes this.
Here, you will practice multiplying and dividing decimals by powers of ten.
Do not insert commas in your answers.
That is, type the answer to
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$\,631.47\times 10^3\,$ as
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$\,631470\,$,
not
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$\,631{,}470\,$.