Question

Express 0.5777.......... as fraction in simplest form​

Answer 1

First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x.

100x = 54.54545454...

But, the decimal part of this number is what we called x, so let's subtract it.

100x - x = 54.5454545454... - 0.54545454

Working out both sides, we get

99x = 54

So, x = 54/99. However, we are not finished as the question said "in its simplest form". Either notice that 99 and 54 are both divisible by 9, or that they're divisible by 3 twice and we get the final answer.

x = 6/11

Answer 2

Here Is Your Ans

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0.57777...

0.57.. = 52 / 90 = 26 / 45

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