Question

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

Answer 1

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:

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