Question

How are percentages similar to decimals? How are they different?

Answer 1

See the explanation.

Explanation:

`color(blue)("The teaching bit")`

Lets start by looking at something else. The metric measurement of centimetres. Which is a unit of measurement.

this word can be split up into two parts.

'centi' and 'metres'

As per the 'Dictionary of Science' by Penguin 7th edition it states:
centi- Prefix denoting one hundredth; `10^(-2)`

So centimetre is the same as `color(green)(1/100" of 1 metre.")`
The whole thing being a unit of measurement.

Thus in this case `1/100` is likewise part of a unit of measurement.

Now compare to percentage.

Suppose we had say `6%` of 1 metre.

This is the same as `6/100` of 1 metre

Is the same as `6xx1/100` of 1 metre

Thus % (`%->1/100`) is part of a unit of measurement and the 6 is a count
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`color(blue)("Answering the question")`

Percentage is a fraction but a special one.
In that the denominator is always 100.

The direct relationship between percentage and decimal is that the overall value is the same. As long as the numbers match.

The difference is in the denominators.

Using an example: say 20%

As a percentage this is `20/100`

As a decimal this is: `(20-:100)/(100-:100) = 0.2/1`

The denominator of 1 is normally ignored and the whole thing written as just 0.2