# convert 0.53 (repeating) to a fraction [Solved] 8/15

Let y = f(x) = x/10, x = 5, x = 1/3 = dx.
So x x = 5 = 5.33333
f(x x) = 5.33333./10 = 0.5333333.
So, were trying to find a rational expression for f(x x).
Since f(x) = y:
y = f(x x) f(x)
And since x = 5, we have f(5) y = f(x x).
Now set up a differential equation:
dy/dx = f'(x)
dy = f'(x) dx
Weve already established that dx = x. Also, for very small values of x, y dy. Now lets solve our differential equation:
y dy = f'(x) dx
y dy = (1/10)(1/3) = 1/30
So remember, were trying to find a rational expression for f(x x). Since 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 y = f(x) = x/10, x = 5, x = 1/3 = dx.
So x x = 5 = 5.33333
f(x x) = 5.33333./10 = 0.5333333.
So, were trying to find a rational expression for f(x x).
Since f(x) = y:
y = f(x x) f(x)
And since x = 5, we have f(5) y = f(x x).
Now set up a differential equation:
dy/dx = f'(x)
dy = f'(x) dx
Weve already established that dx = x. Also, for very small values of x, y dy. Now lets solve our differential equation:
y dy = f'(x) dx
y dy = (1/10)(1/3) = 1/30
So remember, were trying to find a rational expression for f(x x). Since 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.

So 0.533333 = 0.5 0.03333330.5 0.3333/10 = 1/2 (1/3)/10 = 1/2 1/30 = 16/30 = 8/15

So 100x = 53.3333333333
and 10x = 5.3333333333 SUBTRACT

90x = 53 5 = 48.

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

Note: I appreciate Stat Analysts approach. It may be a bit over-your-head. HOWEVER, within it is a key to a different way of doing this. You have to already know that 0.3333 = . and that 0.5 = .

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Let y = f(x) = x/10, x = 5, x = 1/3 = dx.
So x x = 5 = 5.33333
f(x x) = 5.33333./10 = 0.5333333.
So, were trying to find a rational expression for f(x x).
Since f(x) = y:
y = f(x x) f(x)
And since x = 5, we have f(5) y = f(x x).
Now set up a differential equation:
dy/dx = f'(x)
dy = f'(x) dx
Weve already established that dx = x. Also, for very small values of x, y dy. Now lets solve our differential equation:
y dy = f'(x) dx
y dy = (1/10)(1/3) = 1/30
So remember, were trying to find a rational expression for f(x x). Since 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.

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

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

Source(s): : D Does that answer it
Here is the next one too.
53333/100,000

This post is last updated on hrtanswers.com at Date : 1st of September – 2022