Decimal to fraction

Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.

Result

A =  5183
B =  600

Solution:

8.638333333=AB  8.638333333=8.638+3⋅10−4+3⋅10−5+3⋅10−6+....=  =86381000+3⋅10−4⋅11−1/10=  =86381000+3⋅10−4⋅109=  =86381000+310000⋅109=  =86381000+39000=  =5183600  8.638333333=5183600  A=5183 B=600 8.638333333 = \dfrac{A}{B} \ \\ \ \\ 8.638333333 = 8.638 + 3 \cdot 10^{ -4}+ 3 \cdot 10^{ -5} + 3 \cdot 10^{ -6} + .... = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + 3 \cdot 10^{ -4} \cdot \dfrac{1}{1-1/10} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + 3 \cdot 10^{ -4} \cdot \dfrac{10}{9} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + \dfrac{ 3 }{ 10000 } \cdot \dfrac{10}{9} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + \dfrac{ 3 }{ 9000 } = \ \\ \ \\ = \dfrac{ 5183 }{ 600 } \ \\ \ \\ 8.638333333 = \dfrac{ 5183 }{ 600 } \ \\ \ \\ A = 5183 \ \\ B = 600 \ \\

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