I am trying to figure out how to convert the repeating decimal of 4.54 into a fraction.

- Take the repeating part.   Write it in the numerator of a fraction.

- In the denominator, write the same number of ’ 9s ’ as the number of digits
in the numerator.

- There’s your equivalent fraction.   Reduce (simplify) it, if it can be simplified
and if you feel like it.

In your question, the repeating part is ’ 54 ’.

Make the fraction  ’ 54 / 99 ’.

It can be simplified (reduced) to  ’ 6 / 11 ’.

So  4.54 = 4 and 6/11.

X = 4.54545454

* multiply by a power of 10 to get the repeating fraction to the left of the decimal enough that the values to the right of the decimal end up canceling out (see next few steps to understand what this means) - in this case, multiply by 100:

100x = 454.54545454

Now you have 2 equations:

1) 100x = 454.54545454
2)        x = 4.54545454

*subtract equation 2) from 1)

100x - x = 454.54545454 - 4.54545454

99x = 450

*see now how we were able to subtract out the values to the right of the decimal. this makes solving for ’x’ as a fraction easy to deal with, now divide both sides by 99 to isolate ’x’:

x = 450/99

* now simply the fraction, quickest way to do this one is to divide both sides by 9, and it can’t be reduced further, so you have your answer as a fraction

x = 50/11

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