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## What is .277777 repeating the 7 as a fraction?

The cycle repeats at every decimal (cycle = 1)

therefore we will use a factor of 10^1 = 10

step 1)

Keep only the repeating cycle after the decimal point:

0.2777777777 = 2 + 0.777777777/10

step 2)

find out what 0.777777… is:

let p/q be a rational number (a fraction where p and q are integers)

p/q = 0.77777777777

multiply both sides by 10^1 (this is where we use the cycle length)

10(p/q)= 7.77777777….

take away one (p/q) from the ten:

10(p/q) – (p/q) = 7.7777777777… – 0.7777777777…

9(p/q) = 7

p/q = 7/9

step 3)

rebuild the original number:

0.2777777… = 0.2 + 0.777777 / 10 = 0.2 + (7/9)/10 = 2/10 + 7/90 = 18/90 + 7/90 = 25/90 = 5/18

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How to Convert between Fractions and Repeating Decimals – dummies – 0.7 is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say 0.7 repeating, you mean that the 1 is repeating. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating.What is 0.7 7 repeating as a fraction???? decimal to fraction. asked May 23, 2019 in Fraction Problems by kmoney. asked Nov 29, 2019 in Fraction Problems by anonymous | 539 views.A fraction in lowest terms with a prime denominator other than 2 or 5 (i.e. coprime to 10) always produces a repeating decimal. The length of the repetend (period of the repeating decimal segment) of 1/p is equal to the order of 10 modulo p.

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