How do you convert $0 . ¯ ¯¯ ¯ 45$ $0.bar(45)$ (meaning the $45$ $45$ is being repeated) to a fraction?

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Answer 1 · 2018-06-27T17:06:24

$0.45454545.............=5/11$

Let $x=0.45454545.............$ ............................(1)

then $100x=45.45454545............$ ............................(2)

subtracting (1) from (2) we get

$99x=45$

or $x=45/99=5/11$

Hence $0.45454545.............=5/11$

Answer 2 · 2018-06-28T23:35:19

$5/11$

When two numbers in a decimal sequence repeat forever, the denominator will be $11$ .

To think about the numerator, let's just take the number $45$ .

This number would round to $50$ or $5$ tens. Whatever number of tens the numerator rounds to, this will be our numerator.

Thus, we have

$5/11$

Hope this helps!

How do you convert 0.bar(45)0.¯¯¯¯450.bar(45) (meaning the 454545 is being repeated) to a fraction?