Question 319167
I'm assuming that the number is 5.246246246... where the '246' repeats forever.



Let {{{x=5.246246246}}}. Now multiply both sides by 1000 to get {{{1000x=5246.246246246}}}. Why 1000? I wanted to move the decimal point to the next start of the block 246



Now subtract 'x' from 1000x to get {{{1000x-x=5246.246246246-5.246246246=5241}}}



Note: notice how the decimal parts match perfectly and they subtract and cancel out completely.



So we now know that {{{1000x-x=5241}}}



{{{1000x-x=5241}}} Start with the given equation.



{{{999x=5241}}} Combine like terms on the left side.



{{{x=(5241)/(999)}}} Divide both sides by {{{999}}} to isolate {{{x}}}.



{{{x=1747/333}}} Reduce.



----------------------------------------------------------------------


Answer:


So the solution is {{{x=1747/333}}}



Since we let {{{x=5.246246246}}}, this then means that {{{1747/333=5.246246246}}} where the '246' block repeats forever.