How do you convert 1/12 into a decimal and percent?

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How do you convert 1/12 into a decimal and percent?

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Answer 1 · 2017-01-22T16:23:42

$8 \frac{1}{3} % \to 0.0833 ¯ 3$ $8 1/3% " "->" "0.0833bar3$

Explanation:

Lets do it the other way round and determine the % first.

% is like a unit of measurement and is worth $\frac{1}{100}$ $1/100$

So $x %$ $x%$ is the same as $x \times \frac{1}{100} = \frac{x}{100}$ $x xx1/100=x/100$
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$Concept behind method$ $color(blue)("Concept behind method")$

Initial condition $\to \frac{1}{12}$ $->" "1/12$ but we need $\frac{x}{100}$ $x/100$ so the 12 needs to be changed into 100.

First divide it by 12 to make 1 then multiply by 100 to make 100.

$12 \times \frac{1}{12} \times 100 \to 12 \times \frac{100}{12}$ $12xx1/12xx100 -> 12xx100/12$
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$The actual calculation for percentage$ $color(blue)("The actual calculation for percentage")$

To maintain proportionality what you do to the bottom you do to the top (for multiply of divide).

Multiply top and bottom by $\frac{100}{12}$ $100/12$

Initial condition $->" "1/12 -> (" "1xx100/12" ")/(12xx100/12) = (8.333...)/100$

$8.333...$ is the same as $8 1/3$

So we have $8 1/3%$ as an exact value
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$color(blue)("Converting this to a decimal value")$

We have $8.3333... -:100 = 0.083333...$

The 3's repeat for ever and a way of writing this is: $0.083bar3$
where the bar over the last 3 means that it is repeated for ever.

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How do you convert 1/12 into a decimal and percent?

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