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RSB [31]
3 years ago
5

Write $\frac{99}{100}\cdot(0.\overline{4})$ as a fully simplified fraction.

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
6 0

Answer:

  • \frac{11}{25}

Explanation:

The expression that must be rewritten as a fully simplified fraction is:

  • \frac{99}{100}\cdot(0.\overline{4})

You must, first, convert     0.\overline{4}    as a fraction.

The line over the decimal 4 means that the digit 4 repeats indefinetly.

To find the fraction that represents this number you follow this procedure:

F=0.\overline 4\\ \\ 10F=4.\overline 4\\ \\ 10F-F=4\\ \\ 9F=4\\ \\ F=4/9

Now, you can mutiply both fractions:

\frac{99}{100}.\frac{4}{9}=\frac{99\times 4}{100\times9}=\frac{11}{25}

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