How do you convert #0.bar(45)# (meaning the #45# is being repeated) to a fraction?

2 Answers
Jun 27, 2018

Answer:

#0.45454545.............=5/11#

Explanation:

Let #x=0.45454545.............# ............................(1)

then #100x=45.45454545............# ............................(2)

subtracting (1) from (2) we get

#99x=45#

or #x=45/99=5/11#

Hence #0.45454545.............=5/11#

Jun 28, 2018

Answer:

#5/11#

Explanation:

When two numbers in a decimal sequence repeat forever, the denominator will be #11#.

To think about the numerator, let's just take the number #45#.

This number would round to #50# or #5# tens. Whatever number of tens the numerator rounds to, this will be our numerator.

Thus, we have

#5/11#

Hope this helps!