Question

How do you convert 5/7 into a decimal and percent?

Answer 1

Long divide to find:

`5/7 = 0.bar(714285)`

`71.bar(428571) %`

Explanation:

Long divide `5` by `7`, stopping when the remainder repeats:

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 `100`...

`0.bar(714285) * 100 = 71.bar(428571)`

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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.