What is 0.69 expressed as the quotient of two integers in simplest form? (in 0.69 69 repeats)

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Question

What is 0.69 expressed as the quotient of two integers in simplest form? (in 0.69 69 repeats)
 
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campbell_st · Answer

ok... to do this 

let x = 0.6969696969... Equation 1

multiply both sides of the equation by 100

100x = 69.69696969696.... equation 2



now do the subtraction... equation 2 - equation 1

100x = 69.696969696...
      x =   0.696969696...
-------------------------    the subtraction eliminated the recurring decimal




I'll let you finish and find the answer.

anonymous · Answer

2/3?

anonymous · Answer

@campbell_st

campbell_st · Answer

what do you get when you do the subtraction.... and its not 2/3

campbell_st · Answer

100x = 69.69696969...
-       x =   0.69696969...
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anonymous · Answer

69.0000000069

campbell_st · Answer

close

100x = 69.6969696969...
      x =   0.6969696969...
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99 x = 69 


doing the subtraction will eliminate the recurring decimal.... 

now if you solve for x, you will get your fraction.