Question

convert recurring decimal number into vulgar fraction

Answer 1

Take a look at 0.4588888888… This isn’t simply something divided by 99.. since the 45 bit doesn’t repeat. What we need to do is move the decimal point over to the start of the repeating bit. In this case we multiply by 100 to get 45.888888…

Now we know the fraction part is 8/9 . In total we have 45 + 8/9 =  413/9 (changing into a top-heavy fraction will make things easier for us).

So 45.88888… =4.13/9

Now just divide both sides by 100 to get:  0.458888… =

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