What is the proper way to derive percentage from decimal

Question

I have been thinking about this for a while, and I want to know what the proper way to convert a decimal into a percentage is. Say you have a word problem that needs you to convert a decimal, say for instance 0.7, into a percentage. There would be 2 ways to do it:

0.7*100%=70%

or

0.7*100=70%

which is more correct? The first way has the flaw in which 100%=1. So the equation should rightfully be 0.7*100%=0.7. However in the second equation, the percentage is removed but the percentage sign at the very end of the equation pops up without warning. Which would be the proper way to calculate percentage in a word problem.

Answer 1

It might be helpful to keep in mind:

• The term percent is just a shorthand for hundredth, i.e. $\frac{1}{100}$. So whenever you say x percent this is the same as when saying: x-hundreth.

It follows $\color{blue}{0.7\cdot100\%}=0.7\cdot100\cdot\frac{1}{100}=\frac{70}{100}\color{blue}{=70\%}$ is correct, while the second statement is false.

Answer 2

If it would make you more confident in your conversions, you could write $$ (0.7 \times 100)\% = 70\%. $$

Answer 3

You can just write $$ .7 = 70/100 = 70\%. $$ In other words, $70\%$ is literally just another notation for the number $70/100$, or $.7$.

Instead of saying, "$70\%$ of the cars are blue", it would be equally valid (if a bit strange-sounding) to say, "$.7$ of the cars are blue."