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avatar+764 

Express 0.\overline{2123} as a base 10 fraction in reduced form.

 Jun 15, 2024

Best Answer 

 #2
avatar+1252 
+1

In order to solve this problem, we can use a very simple trick. 

First, let's set \(x = 0.\overline{2123}\)

 

If we have this for the value of x, we get \(10000 x = 2123.\overline{2123}\)

 

Now, we subtract x from 10000x. We get

\(10000x-x= 2123.\overline{2123} -\overline{2123}\\ 9999x=2123\)

 

This means we get

\(x = \frac{2123}{9999}\)

 

Simplifying, we get

\(x = \frac{193}{909}\)

 

So our final answer is \( \frac{193}{909}\)

 

Thanks! :)

 Jun 16, 2024
 #1
avatar+1714 
0

The answer is 17/210.

 Jun 15, 2024
 #2
avatar+1252 
+1
Best Answer

In order to solve this problem, we can use a very simple trick. 

First, let's set \(x = 0.\overline{2123}\)

 

If we have this for the value of x, we get \(10000 x = 2123.\overline{2123}\)

 

Now, we subtract x from 10000x. We get

\(10000x-x= 2123.\overline{2123} -\overline{2123}\\ 9999x=2123\)

 

This means we get

\(x = \frac{2123}{9999}\)

 

Simplifying, we get

\(x = \frac{193}{909}\)

 

So our final answer is \( \frac{193}{909}\)

 

Thanks! :)

NotThatSmart Jun 16, 2024

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