# Converting Recurring Decimal Into a Fraction

I'm confused. I know the method and have been trying to convert 0.0999999 but
keep coming up with 1/10 as the answer which doesn't feel right given that 1/10
is 0.1 as a decimal. Here's the method I used,where am I going wrong?

x = 0.099999
100x = 9.9999

100x - x = 99x = 9.9

990x = 99 so x = 1/10!!!!

### Comments for Converting Recurring Decimal Into a Fraction

 May 10, 2011 Converting Recurring Decimal into a Fraction by: Staff The question: I'm confused. I know the method and have been trying to convert 0.0999999 but keep coming up with 1/10 as the answer which doesn't feel right given that 1/10 is 0.1 as a decimal. Here's the method I used,where am I going wrong?x = 0.099999100x = 9.9999100x - x = 99x = 9.9990x = 99 so x = 1/10!!!!The answer: Even though it shouldn’t be that way . . . Even though it is hard to believe, you are entirely correct.0.099999… = 1/10>>>>>>>>>> The number of digits used to represent a number depends entirely on the numbering system:>>>>>Example 1Using the number base of 10½ (base 10) = 0.5 (base 10)But when this same number is expressed using the number base of 2½ (base 10) = 0.011111111111111111111111111111111111111111111111111111 (base 2)Or when this same number is expressed using the number base of 7½ (base 10) = 0.3333333333333333333532345065211213525246152246304514464052022156340626024455016523433003404232432654 (base 7)Example 22/5 (base 10) = 0.4 (base 10)But when this same number is expressed using the number base of 52/5 (base 10) = 0.2 (base 5)Or when this same number is expressed using the number base of 42/5 (base 10) = 0.121212121212121212121212122 (base 4)Thanks for writing.Staff www.solving-math-problems.com