Percentages, Part 1

I am confident that the chance of you liking this post is 100%. But what does 100% mean? I will talk about this in the next few posts.

First let’s review what a fraction is. The fraction

$\frac{3}{4}$

means that I have 3 pieces (the numerator) of some whole thing that was divided into 4 pieces (the denominator). So the denominator sets the size of the pieces (the bigger the denominator, the smaller the pieces) and the numerator sets how many pieces.

Being creatures that have 10 fingers, we naturally migrate to things that are powers of 10. Way back in the Roman empire days (I remember them fondly), the Romans frequently used fractions that had a denominator of 100. In fact, the word “percentage” comes from the latin (Roman) per centum which means “by the hundred”. That has continued to today, as a percentage is really a fraction where the denominator is fixed at 100. What you see in a percentage is the numerator:

${37}{\%}\hspace{0.33em}{=}\hspace{0.33em}\frac{37}{100}$

So a percentage like 37% means that if I divide something into 100 equal pieces, I have 37 of these pieces. Percentages are also used to indicate a probability. My first sentence in this post used a percentage in this way. If you remember, a probability of an event is a fraction. The probability of event A is expressed as P(A):

${P}{(}{A}{)}\hspace{0.33em}{=}\hspace{0.33em}\frac{{\mathrm{Number}}\hspace{0.33em}{\mathrm{of}}\hspace{0.33em}{\mathrm{times}}\hspace{0.33em}{\mathrm{event}}\hspace{0.33em}{\mathrm{A}}\hspace{0.33em}{\mathrm{occurs}}}{{100}\hspace{0.33em}{\mathrm{trials}}}$

So 100% of you liking this post means that if I take 100 random people who have read this post, 100 of them will like this post. This means all will like this post as that is what 100% means: the whole:

${100}{\%}\hspace{0.33em}{=}\hspace{0.33em}\frac{100}{100}\hspace{0.33em}{=}\hspace{0.33em}{1}$

Now percentages, fractions, and decimals are all ways to express a part of something. In my next post, I will show how to convert percentages to fractions and decimals and vice versa.