Asked by math

Write .4(5) as a fraction.

The parenthesis represent it as a repeating decimal:
.455555555555555555555
But what is it in a fraction?

11 years ago

Answered by Damon

.4 + 5/100 + 5/1000 + 5/10,000.......

.4 + 5/100 +(5/100)(1/10) ..

.4 + infinite geometric series with a = 5/100 and r = 1/10

.4 + sum of series

.4 + a/(1-r)

.4 + 5/100 / (9/10)

4/10 + (5/9)/ 10

(4 5/9 )/10

41/90

11 years ago

Answered by Damon

my calculator says yes that works :)

11 years ago

Answered by math

thanks DAMON

11 years ago

Answered by Damon

You are welcome :)

11 years ago

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