Percents As Ratios

How treating percents as ratios can simplify your work

What is a percent?

Percent means parts per hundred parts:

There are 100 stars here.

There are 3 red stars per hundred total, or 3% of the stars are red.

There are 97 yellow stars per hundred total, or 97% of the stars are yellow.

There are 300 stars here.

There are 9 red stars per three hundred total.

9/300 = 3/100

3% of the stars are red.

There are 291 yellow stars per three hundred total.

291/300 = 97/100

97% of the stars are yellow.

Percents ARE ratios

Let’s try to picture, instead, ‘per cent’ or:

%

When most of us think about percents, we picture:

perhundred

Continue….

How does this help?

Problem 1:Write 75% as a fraction:

Easy!!“3/4”Who needs ratios??

Continue….

Problem 2:Write 0.0196% as a fraction:

Huh?

Continue….

Problem 2:Write 0.0196% as a fraction:

Wait…0.0196% is 0.0196 per cent

Continue….

Problem 2:Write 0.0196% as a fraction:

0.0196 100

0.0196 per cent is:0.0196 per hundred or 0.0196 100

Hurray!

Problem 3:Convert 0.017 to a percent.

I bet you can use ratios for this too…

Continue…

Problem 3:Convert 0.017 to a percent.

I want to know…0.017 = ? percent, or ? per hundred: 0.017 = ? 100

Solve…

Problem 3:Convert 0.017 to a percent.

1.7%

0.017 = ? 100

(0.017)(100) = ?1.7 = ?

So: 0.017 = 1.7/100 or 1.7%

Hurray!

Percents QuizWrite 0.816% as a fraction:

Write 0.12 as a percent:

Continue…

Percents QuizWrite 0.816% as a fraction:

0.816 100

Write 0.12 as a percent:0.12 = ?

10012 = ?

0.12 = 12%