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How can you convert 0.99999999999999999999... to a fraction?

Guest Mar 8, 2015

Best Answer 

 #2
avatar+92623 
+5

It is 1

$$let x=0.\bar{9}$$

 

10x=9.9999999999999...

    x=0.999999999999.....

subtract

 9x = 9

x=9/9

x=1

Melody  Mar 9, 2015
 #1
avatar
0

Consider that

$${\frac{{\mathtt{0.9}}}{{\mathtt{10}}}} = {\frac{{\mathtt{9}}}{{\mathtt{100}}}} = {\mathtt{0.09}}$$

 

and that

$${\frac{{\mathtt{0.99}}}{{\mathtt{100}}}} = {\frac{{\mathtt{99}}}{{\mathtt{10\,000}}}} = {\mathtt{0.009\: \!9}}$$

Guest Mar 9, 2015
 #2
avatar+92623 
+5
Best Answer

It is 1

$$let x=0.\bar{9}$$

 

10x=9.9999999999999...

    x=0.999999999999.....

subtract

 9x = 9

x=9/9

x=1

Melody  Mar 9, 2015

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