How do you convert 0.45 (45 repeating) to a fraction?

2 Answers
May 10, 2016

#0.454545... = 45/99 = 5/11#

Explanation:

Short cut: #(" write down the recurring digits")/("write a 9 for each recurring digit")#

Long Method:

#"Let" x = 0.454545....#
# 100x = 45.454545..... " 2 recurring digits" rArr xx 100#

#99x = 45.000000..... " the decimals all subtract to 0"#

#x = 45/99#

Simplify if possible.

May 10, 2016

You have to write a systems of equations, in one variable, to represent this problem.

#100x = 45.bar(45)#
#x = 0.bar(45)#

Now, subtract, like you would do to solve a systems of equations by elimination.

#99x = 45#

#x = 45/99#

#x = 5/11#

Therefore, #0.bar(45)# as a fraction is #5/11#

Hopefully this helps!