How do you convert 1/3 into a decimal and percent?

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Answer 1 · 2016-05-21T11:34:00

$\frac{1}{3}$ $1/3$ as a decimal $\to 0.3 ¯ 3$ $->0.3bar3$

$\frac{1}{3}$ $1/3$ as a percentage $\to \frac{33.3 ¯ 3}{100} \to 33.3 ¯ 3 %$ $->(33.3bar(3))/100 -> 33.3bar(3)%$

$Determining the decimal value of \frac{1}{3}$ $color(blue)("Determining the decimal value of "1/3)$

If you apply long division you soon observe a repeating pattern. You would have demonstrated that this pattern goes on forever. The number is:

$0.3333333333333.....$

The mathematical way to show the repeating process is to put a bar over the last 3 that you write. So you would get:

$0.3bar3$
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Determining the percentage equivalent of "1/3)$

The first decimal place is $1/10color(white)()^("ths")$

The second decimal place is $1/100color(white)()^("ths")$

As percentage is really $1/100color(white)()^("ths")$ then we would write:

$(33.3bar(3))/100 -> 33.3bar(3)%$