Question

Which simplified fraction is equal to 0.53 (the 3 is repeating)

Answer 1

Answer: B
explanation: just divide 8/15

Answer 2

Answer:  Choice B. 8/15

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Explanation:

x = 0.53333333... the 3's go on forever

10x = 5.3333333..... we have infinitely many 3's here as well

100x = 53.333333..... same story

Each time we multiply both sides by 10, we move the decimal point over 1 spot to the right.

Focus on this system of equations

$\begin{cases}100x = 53.33333\ldots\\\ \ \ 10x = 5.333333\ldots\end{cases}$

Note how the decimal points line up so we can see both right sides have the same 33333... pattern

If we subtract those equations straight down, the left hand side turns into 90x because 100x-10x = 90x

The right hand side terms subtract to 48. The infinite number of 3's after the decimal will cancel out when we subtract. So we basically have 53-5 = 48.

After those subtractions, we now have the new equation 90x = 48

Divide both sides by 90 and reduce

90x = 48

90x/90 = 48/90

x = 48/90

x = (6*8)/(6*15)

x = 8/15

8/15 = 0.53333333....