Math Is Fun Forum

cknowlton50

Member

Registered: 2015-01-12

Posts: 1

Find the rational number (ratio) for a repeating decimal

How do you find the rational number for a repeating decimal?

example:  0.22222...
              0.37373737...

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Find the rational number (ratio) for a repeating decimal

Here is an algorithm.

I will do the second example for you

Let the number be x
x=0.373737...  [Call this equation 1]
Or, 100x = 37.373737... [Call this equation 2]

Subtract equation 1 from equation 2: 100x - x = 37.3737... - 0.3737....
Or, 99x=37
Or, x=37/99

So, the answer is 37/99

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