How do you convert 6.125 (25 repeating) to a fraction?

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Answer 1 · 2016-12-22T22:04:25

This decimal can be written as: #6 62/495#. See explanation.

To simplify the calculation let's isolate integer part, non repeating decimal and the period:

#6.1bar(25)=6.1+0.0bar(25)#

Now we can calculate the repeating part separately:

#0.0bar(25)=0.025+0.00025+ ...#

From the calculations we see that the fraction is a sum of a convergent geometrical sequence with:

First term #a_1=0.025# and ratio: #r=0.01#.

So the sum of the sequence is:
#S=a_1/(1-r)=0.025/(1-0.01)=0.025/0.99=25/990#

So the value of fraction is:

#6.1bar(25)=6.1+25/990=6+1/10+25/990=6 + 99/990+25/990=6 124/990=6 62/495#