Converting a Repeating Decimal to a FractionDate: 9/10/96 at 3:28:58 From: Anonymous Subject: Converting Repeating Decimal to Fraction A simple way to convert a recurring decimal to a vulgar fraction is as follows: Example: 0.942424242... Write down the whole fraction, 942. Subtract those digits that don't recur:s 942 - 9 = 933. Then divide by the following number. For every recurring digit write down a 9, and for every non-recurring digit write down a nought after your 9's: 933/990. Why does this work? Date: 9/10/96 at 14:34:54 From: Doctor Ana Subject: Re: Converting Repeating Decimal to Fraction This actually works for a very good reason, but rather than show you why this method works, I'll show you another method for converting repeating decimals to fractions and demonstrate why that works, and then you can try to work on your problem using similar ideas. So here's another way to convert to a fraction. Let's take the decimal 0.759595959... We can break this up into 2 parts as follows: 0.7 + 0.05959595959... and treat each part separately. 7 .7 = -- 10 1 and .0595959... = -- x .595959... 10 So now we have 7 1 0.75959... = -- + -- x .5959... 10 10 Now we can just worry about the repeating part. 59 59 59 .5959... = -- + ---- + ------- ... 100 10,000 1,000,000 This all is actually equal to the following: 59 .5959...= -- 99 because: 59 59 59 -- = -- + -- 99 100 9900 (try it) Then the 59/9900 term can be split up again to 59/10000 + 59/990000, and so on and so on. So, let's put all of the pieces together. 7 1 59 .7595959...= - + -- x -- 10 10 99 7 59 = - + -- 10 990 If you get a common denominator and combine these you should get the same answer (after simplifying) that you get with your method. Now that we have broken the above method into steps and have a sense for why it works, why don't you try to do the same for your method. What happens when you break it into steps? If you need more help, please feel free to write back to us. Good luck! -Doctor Ana, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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