How do you convert 0.12345 (12345 repeating) to a fraction?
2 Answers
Explanation:
Multiply by
#(100000-1) 0.bar(12345) = 12345.bar(12345)-0.bar(12345) = 12345#
Then divide both sides by
#0.bar(12345) = 12345/(100000-1) = 12345/99999 = (color(red)(cancel(color(black)(3)))*4115)/(color(red)(cancel(color(black)(3)))*33333) = 4115/33333#
Explanation:
Require to obtain 2 equations with the same repeating part and subtract them to eliminate the repeating part.
Begin by letting x = 0.1234512345................... (A)
To obtain the same repeating part after the decimal point need to multiply by 100000
hence : 100000x = 12345.1234512345............... (B)
It is important to obtain 2 equations in x , where the recurring part after the decimal point are exactly the same.
Subtracting (A) from (B) will eliminate the repeating part.
(B) - (A) gives : 99999x = 12345
# rArr x = 12345/99999 = 4115/33333#