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Q: What fraction will produce the recurring decimal .71288888888888?

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The number 0.166 recurring where the 166 recurs forever is expressed as a fraction 166/999 or one hundred and sixty-six nine hundred and ninety-ninths.

71,288,888,888,888/100,000,000,000,000 = 8,911,111,111,111/12,500,000,000,000The decimal recurring infinitely is equal to 802/1125.

The numbers that produce recurring numbers are: 3,6,7,9,11,12,13.. Hope this has helped you...

Any fraction is a rational number and by dividing its denominator into its numerator will produce a decimal number as for example 3/4 = 0.75

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Call this number "x", equal to 0.166166166... 1000x = 166.166166166... x = 0.166166166... Subtract the second equation from the first, you get: 999x = 166 Solving for x: x = 166/999. Note: I multiplied by 1000, because three digits are repeating (and 1000 has 3 digits).

Any fraction with a denominator which has a prime factorization that includes any prime other than 2 or 5, it can produce repeating decimals.If the prime factorization of the denominator does not include 2 nor 5 then the decimal representation will be a repeating decimal.

A fraction

In order to add a fraction to a variable the fraction must be converted to decimal as computers cannot understand fractions, thats why they have floating points. On the other hand you could produce an answer in decimal and then convert it into a fraction afterwards but it would be overly complicated for a program to do this. I suggest if you are seriously into this somewhat eccentric behaviour you should try the program Mathematica from Wolfram research which is very expensive.

Multiply by the smallest integral power of 10 to produce an integer from the original number, then use the resulting integer over the power of ten as a fraction. In this specific instance, 4.64 = 464/100 or in lowest terms 116/25.

Multiply by the smallest integral power of 10 to produce an integer from the original number, then use the resulting integer over the power of ten as a fraction. In this specific instance 8.06 X 100 = 806; therefore, the fraction is 806/100 = 403/50 or 8 and 3/50.

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