How do you convert 0.78023 (023 repeating) as a fraction?

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Answer 1 · 2016-03-07T15:04:44

#x=77945/99900#

Given:#" "0.78bar023#

'~~~~~~~~~~~~~~~~~~~~~~~~
Note about formatting: using the 'hash' key

write: hash key 0.78bar023 hash key and you get :#" "0.78bar023#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let #" "x=0.78bar023#

Then #1000x=780.23bar023#

Notice that the repeating parts start in the 3rd decimal place for both#" "x" and "1000x#. Consequently subtraction removes the repeating part.

#1000x-x=779.45#

#x(1000-1)=779.45#

#x=(779.45)/(999)#

But we do not wish to have a decimal numerator

#x=(779.45)/(999) xx 100/100" "=" "77945/99900#