How do you convert 5/7 into a decimal and percent?
1 Answer
Long divide to find:
#5/7 = 0.bar(714285)#
#71.bar(428571) %#
Explanation:
Long divide
Once the remainder repeats then (since there are no new digits to cause other behaviour) the quotient repeats too.
So we have:
#5/7 = 0.714285714285714285... = 0.bar(714285)#
In case you are not familiar with the bar notation: A bar is drawn over a sequence of digits to indicate that they repeat indefinitely.
To convert this into a percentage ("per-hundred-age"), multiply by
#0.bar(714285) * 100 = 71.bar(428571)#
Footnote
An alternative notation that seems to be used less nowadays involves placing a dot above the first and last digit of the repeating sequence.
So in our example:
#0.714285714285714285... = 0.bar(714285) = 0.dot(7)1428dot(5)#
The dots shown by Socratic are rather small, so I tend to avoid using them here, but they can be more convenient than drawing a bar over a long repeating section.