# convert 0.53 (repeating) to a fraction?

How to convert 0.53 (repeat) to fraction?

I think Mark’s answer is excellent, very direct. Let’s do this with the math too (just for fun):

Let y = f(x) = x/10, x = 5, ∆x = 1/3 = dx.
So x + ∆x = 5⅓ = 5.33333…
f(x+∆x) = 5.33333…./10 = 0.5333333….
We are therefore trying to find a rational expression for f(x+∆x).
As f(x) = y:
∆y = f(x+∆x) – f(x)
And since x = 5, we have af(5) + ∆y = f(x+∆x).
Now establish a differential equation:
dy/dx = f'(x)
dy = f'(x) dx
We have already established that dx = ∆x. Also, for very small values ​​of ∆x, ∆y ≃ dy. Let’s now solve our differential equation:
∆y ≃ dy = f'(x) dx
∆y ≃ dy = (1/10)(1/3) = 1/30
So remember, we’re trying to find a regular expression for f(x+∆x). As ∆y ≃ dy, we can write:
f(x+∆x) = f(5) + ∆y ≃ f(5) + dy
f(x+∆x) ≃ f(5) + 1/30 = 1/2 + 1/30 = 16/30 = 8/15.

Let x = 0.5333333333 …

So 100x = 53.3333333333…
and 10x = 5.3333333333… SUBTRACT…
—————————————
90x = 53 – 5 = 48.

So x = 48/90 = 8/15 after reduction to lower terms (by factor of 6)

Note: I like the “Stat Analyst” approach. It may be just above your head. HOWEVER, within it lies the key to a different way of doing it. You may already know that 0.3333… = ⅓. and that 0.5 = ½.

So 0.533333… = 0.5 + 0.0333333…0.5 + 0.3333…/10 = 1/2 + (1/3)/10 = 1/2 + 1/30 = 16/30 = 8 /15

08/15

53 out of 100
Or
533 out of 1000
Or
5333 over 10,000

Here is also the next one.
53333/100,000

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