How do you convert 0.45 (45 repeating) to a fraction?

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Answer 1 · 2016-05-10T18:02:31

$0.454545... = 45/99 = 5/11$

Short cut: $(" write down the recurring digits")/("write a 9 for each recurring digit")$

Long Method:

$"Let" x = 0.454545....$
$100x = 45.454545..... " 2 recurring digits" rArr xx 100$

$99x = 45.000000..... " the decimals all subtract to 0"$

$x = 45/99$

Simplify if possible.

Answer 2 · 2016-05-10T18:03:17

You have to write a systems of equations, in one variable, to represent this problem.

$100x = 45.bar(45)$
$x = 0.bar(45)$

Now, subtract, like you would do to solve a systems of equations by elimination.

$99x = 45$

$x = 45/99$

$x = 5/11$

Therefore, $0.bar(45)$ as a fraction is $5/11$

Hopefully this helps!