Write .4(5) as a fraction.

Question

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

Answer 1

.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

Answer 2

my calculator says yes that works :)

Answer 3

thanks DAMON

Answer 4

You are welcome :)