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Basic Math/Percentages

Question
Hello:

If percentages have no units, why are some percentages called rates, as in interest rates, or perhaps a tax rate of 7% as an example?  A rate has units of different quantities.

Hello Kenneth,

Good question.

In a mathematical sense, rate is a proportion.

So, for example, when we talk about speed, it is the proportion formed by
change in distance and change in time...to give "average rate change" in
miles per hour (i.e. miles divided by hours), for example.

If we talk about money for example, say we are charged \$7 sales tax on a \$100
purchase, the proportion \$7 to \$100 gives 0.07 and dollars divided by dollars
yields a unitless result.  Suppose out of 100 people in a room, 20 of them leave.
So, 20 people out of 100 people (or 20 ppl/100 ppl), or 0.20 = 20% (unitless) left.

So, when we form a proportion (or rate) with the same units, they divide each other
giving a unitless quantity, which is what we typically call a percentage.

I hope this helps.

Abe
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Basic Math

Volunteer

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook