Convert 5.764764764 to a rational expression in the form of a over b , where b ≠ 0

Question

Convert 5.764764764  to a rational expression in the form of a over b , where b ≠ 0

ZombieLover · Answer

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surjithayer · Answer

is it a repeating decimal?

Florisalreadytaken · Answer

so thats a periodic number, or diff said, repeating decimals -- to turn those kinds of numbers into fractions, the denominator should be with a base of 9. the number we have to work with is $5.764764764$ -- we can see that $ 764 $ is the repeated part, so we keep that, and kinda forget about the rest. so the number would be $ 5.\overline{764} $ right?

Florisalreadytaken · Answer

@florisalreadytaken wrote:

so thats a periodic number, or diff said, repeating decimals -- to turn those kinds of numbers into fractions, the denominator should be with a base of 9. the number we have to work with is [color= inherit;][/color]$5.764764764$ -- we can see that [color= inherit;][/color]$ 764 $ is the repeated part, so we keep that, and kinda forget about the rest. so the number would be [color= inherit;][/color]$ 5.\overline{764} $ right?

we should get rid of the decimal part, by turning that into a fraction -- there is 3 decimal digits. if it was a normal decimal number, we would multiply the number by $ 1000 $, but its a periodic number, so take 1 off that 1000, and we get 999. SO we get this $ \frac{5764}{999} $