Question

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

Answer 1

11/25

Step-by-step explanation:

Answer 2

• 
  `(11)/(25)`

Step-by-step explanation:

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

• 
  `(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:

`(99)/(100).(4)/(9)=(99* 4)/(100*9)=(11)/(25)`