Shortcut: Repeating Decimals to Equivalent FractionsDate: 03/24/2001 at 20:05:01 From: Andrew Wan Subject: Shortcut to changing repeating decimals into their equivalent fractions My question is, how do you change a repeating decimal into its equivalent fraction? Actually, I know how to, but is there some kind of shortcut? Date: 03/24/2001 at 23:05:59 From: Doctor Peterson Subject: Re: Shortcut to changing repeating decimals into their equivalent fractions Hi, Andrew. You can read the general method for doing this in our archives: Fractions, Decimals, Percentages - Dr. Math FAQ http://mathforum.org/dr.math/faq/faq.fractions.html It sounds as if you know that, and are looking for something quicker. For simple cases, it can be done without going through all the work. If the repeat starts right after the decimal point, you can just divide the repeat by as many 9's as there are digits in the repeat: _ 3 0.3 = - = 1/3 9 __ 05 0.05 = -- = 5/99 99 ______ 142857 0.142857 = ------ = 1/7 999999 Compare this with the normal method, and you should quickly see why this works: 100x = 5.0505... x = 0.0505... ---- --------- 99x = 5 x = 5/99 When the repeat doesn't start just after the decimal point, you can move it there, do the conversion, and move it back: __ __ 0.1234 = 0.12 + 0.34 / 100 = 12/100 + 34/99 / 100 = 12/100 + 34/9900 = 12*99/9900 + 34/9900 = (1188+34)/9900 = 1222/9900 = 611/4950 As you can see, once you have to do this, you might as well use the usual method: 100x = 12.343434... x = 0.123434... ---- ------------ 99x = 12.22 x = 12.22/99 = 1222/9900 = 611/4950 Suddenly this doesn't seem so hard, does it? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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