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How do you convert 0.7 (7 being repeated) to a fraction?

Answer 1

Isaiah Anthony

#0.bar(7) = 7/9#

With the indication that a repeating digit is represented by a bar,

let #x = 0.bar(7)#

#=> 10x = 7.bar(7)#

#=>10x - x = 7.bar(7)-0.bar(7)#

#=>9x = 7#

#=>x = 7/9#

This technique works in general to find the fractional representation of a repeating decimal. Just multiply by #10^n# where #n# is the number of digits that are repeating, then subtract away the original repeating digit and solve for #x#.

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Answer 2

Abigail Allen

To convert 0.7 (7 being repeated) to a fraction, we can represent the repeating decimal as (0.\overline{7}). To convert this to a fraction, we set it as (x = 0.\overline{7}) and multiply both sides by 10 to shift the repeating decimal to the left by one place, resulting in (10x = 7.\overline{7}). Next, we subtract the original equation from the shifted equation, which gives (10x - x = 7.\overline{7} - 0.\overline{7}). Simplifying, we get (9x = 7), and dividing both sides by 9, we find (x = \frac{7}{9}). Therefore, (0.\overline{7}) as a fraction is (\frac{7}{9}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.