Decimal to fraction

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

Correct 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 

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