1) A "percentage" is just a fancy way to write a fraction over a hundred.

From the Latin: per centum (for a hundred).

25% means EXACTLY the same as 25/100

which is the same as 5/20 and the same as 1/4.

2) When measuring the "fraction" of an increase (or decrease), it is traditional to use the "start" number (before the increase).

Here, this number is 150.

The increase is 50 (200 - 150)

The fraction is, therefore, 50/150, which can be reduced to 5/15 and to 1/3

The trick, now, is to write this fraction (1/3) over one hundred.

The denominator is presently 3, we have to get that to a hundred.

Multiplying it by 33 would give 99 (quite close, but not exactly it)

Multiplying it by 34 would give 102 (still close, but now too much).

So far, we know the answer is between 33% and 34%.

Multiplying the "3" by 33.3 would give us 99.9

and you could continue by adding "3"s to the decimal expansion.

Let's say that 99.9 is "close enough to a hundred" for us.

Then you need to take your original fraction (1/3 = 50/150), and multiply it -- above and below, so as not to change its value -- by 33.3

1/3 = (1/3)(33.3/33.3) = 33.3/99.9

which we can call 33.3%

since we convinced ourselves that 99.9 was close enough to 100.

If not, you can continue to tack on extra "3"s.

33.333333333... % (as many "3"s as you can stand

There comes a time when adding "3"s really does not add useful information. After all, there is no such thing as a tenth of a penny, when paying rent.

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Some people might write 33 1/3 %

That too is OK. It is "more accurate" but not more useful.

They are all fancy ways of writing the value of the fraction 1/3 as a "fraction over a hundred".