How do you write 0.3666... as a fraction? The 6 repeating.

3 Answers
Jan 2, 2018

18333/50000

Explanation:

Put the number over 1( make denominator 1)
0.36666/1
and multiply by 10 for every number after the decimal point.
as there is 5 numbers you have to multiply by 100000
=(0.36666*100000)/(1*100000)

=36666/100000
and divide by the greatest factor, which is 2

=(36666/2)/(100000/2)

=18333/50000 final answer.

Jan 2, 2018

See a solution process below:

Explanation:

First, we can write:

x = 0.3bar6

Next, we can multiply each side by 10 giving:

10x = 3.bar6

Then we can subtract each side of the first equation from each side of the second equation giving:

10x - x = 3.bar6 - 0.3bar6

We can now solve for x as follows:

10x - 1x = (3.6 + 0.0bar6) - (0.3 + 0.0bar6)

(10 - 1)x = 3.6 + 0.0bar6 - 0.3 - 0.0bar6

9x = (3.6 - 0.3) + (0.0bar6 - 0.0bar6)

9x = 3.3 + 0

9x = 3.3

(9x)/color(red)(9) = 3.3/color(red)(9)

(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = (3 xx 1.1)/color(red)(3 xx 3)

x = (color(red)(cancel(color(black)(3))) xx 1.1)/color(red)(color(black)(cancel(color(red)(3))) xx 3)

x = 1.1/3

x = 10/10 xx 1.1/3

x = 11/30

Jan 2, 2018

0.366...=11/30

Explanation:

There's nice algebraic trick to get rid of repeating tail:

x=0.366...

10x=3.666...

10x-x=3.6cancel(66...)-0.3cancel(66...)

9x=3.6-0.3=3.3

90x=33

x=33/90=11/30

If there's n digits in repeating element, then multiply by 10^n

x=0.36565...

100x=36.56565...

100x-x=36.5cancel(6565...)-0.3cancel(6565...)

99x=36.5-0.3=36.2

990x=362

x=362/990=181/495