How do you convert #0.bar5# (5 repeating) as a fraction?

Need to create two equations with the same repeating element and subtract them in order to get rid of the repetition.

start by allowing x to equal 0.5555555. (1)

You must multiply by ten to get the same repeating portion after the decimal point.

Consequently, 10x = 5.555555..(2)

Getting two equations in x that have the exact same recurring portion after the decimal points is crucial.

now, to obtain the fraction, subtract (1) from (2).

To convert the repeating decimal 0.bar5 (where "bar5" indicates that the digit 5 repeats infinitely) to a fraction, you can use the following method:

Let x = 0.bar5

Multiply both sides by 10 to shift the decimal one place to the right: 10x = 5.bar5

Subtract the original equation from the shifted equation: 10x - x = 5.bar5 - 0.bar5 9x = 5

Divide both sides by 9 to solve for x: x = 5/9

So, 0.bar5 is equal to 5/9 as a fraction.