Convert the decimal 0. bar(6) to a fraction by writing it as an infinite series. 0. bar(6) =

Gauge Roach

Gauge Roach

Answered question

2022-08-06

Convert the decimal 0. 6 ¯ to a fraction by writing it as an infinite series. 0. 6 ¯ =

Answer & Explanation

Bradley Forbes

Bradley Forbes

Beginner2022-08-07Added 12 answers

0. 6 ¯ = 0.6666666 = 0.6 + 0.06 + 0.006 + 0.006 +
This repeating decimal can be considered as an infinite geometric series with the first term ( a 1 ) being 0.6 and the common ratio(r) being 1/10 or 0.1
For an infinite geometric series of the form a 1 + a 1 r + a 1 r 2 + the sum of the terms of the series is given by,
S = a 1 ( 1 r )
a 1 = 0.6 and r = 0.1
S = 0.6 ( 1 0.1 ) = 0.6 0.9 = 6 9 = 2 3
S = 2 3
So the fraction equivalent is 2 3

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