How do you convert 1.37 (7 being repeated) to a fraction?

3 Answers
Mar 17, 2016

#62/45#

Explanation:

We first let 1.37 (7 being repeated) be #x#.

Since #x# is recurring in 1 decimal places, we multiply it by #10^1#.

#10x = 13.77#

Next, we subtract them.

#10x - x = 13.77 - 1.37#

#9x = 12.4#

Lastly, we divide both sides by 9 to get #x# as a fraction.

#x = 12.4/9#

#= 124/90#

#= 62/45#

Mar 18, 2016

Let #x=1.377777777....#, then

#10x=13.77777777...# and
#100x=137.777777777---#

Subtracting 2nd equation from third, we get

#90x=124#

#x=124/90=62/45#

Mar 18, 2016

x=45/62

Explanation:

_

1.37
x=1.37
10x=13.7
100x=137.7
100x-10x=137.7-13.7
90x=124
x=124/90
x=45/62