Math CentralQuandaries & Queries


Question from Ruth:

what does the 0 represent in .018 versus the decimal .180? As in, changing these to fractions? Thank you.

Hi Ruth,

The 0 in the two decimal representations of the numbers have different place values. Below is a place value chart.

place value chart

Below I have written the decimal number 0.645 in the place value chart.


Since 6 is in the tenths place it represents $\large \frac{6}{10}.$

Since 4 is in the hundredths place it represents $\large \frac{4}{100}.$

Since 5 is in the thousandths place it represents $\large \frac{5}{1000}.$


\[0.645 = \frac{6}{10} + \frac{4}{100} + \frac{5}{1000}.\]

Writing this with a common denominator I get

\[0.645 = \frac{6 + 40 + 500}{1000} = \frac{645}{1000}.\]

This fraction can be simplified.

In a similar fashion

\[0.108 = \frac{1 + 0 + 800}{1000} = \frac{108}{1000}.\]

This fraction can also be simplified.

I hope this helps,

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