The original question was to convert 0.31(repeating) base 5, to a fraction in base 10 in its lowest form, however, after solving about half of it, you would get this fraction and you must try to convert it into a base 10 form.
2026-04-01 15:59:34.1775059174
How do you convert fractions from one number base system to another? Like for example 31/44 base 5 to a base 10 number...
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You can convert the numerator and denominator individually to base 10 and then simplify the resulting fraction. Computing this out, we get $\left( \frac{31}{44} \right)_5 =\left( \frac{16}{24} \right)_{10} = \frac{2}{3}$ in base 10.
If this seems confusing, remember that the fraction in question is the solution to the equation $44_{5}x = 31_{5}$. The solution to this equation $x$ is the same number, regardless of which base it's expressed in. Changing which base the numerator and denominator are in doesn't affect the value of the fraction itself at all.