Lesson 3  Section 2

The Meaning of Percent

The student should first understand Section 1: Multiplying and Dividing by Powers of 10.

Thus, 100% means 100 for each 100, which is to say, all.  100% of 12 is 12.

50% is another way of saying half, because 50% means 50 for each 100, which is half.  50% of 12 is 6.

Percent, which is so many for each 100, is a number of hundredths.

Example 1.   Below are 100 small squares, and 32 have been shaded.

What percent of the squares have been shaded?

Answer.   32% -- 32 for each 100.  32 hundredths.

When the percent is less than or equal to 100%, then we can say "out of" 100.  32% is 32 out of 100.  But to say that 200% is 200 out of 100 makes no sense.  200% is 200 for each 100, which is to say, twice as much.

Example 2.   100 people were surveyed, and 65 responded Yes.  What percent responded Yes?

Answer.   65% -- 65 out of 100.

Example 3.   In a class of 30 students, all 30 came to school by bus. What percent came to school by bus?

Answer.   100%.  100% means all.

(30 out of 30 is equivalent to 100 out of 100.)

In other words, 1% is the hundredth part of 100%. (Lesson 2.)

10% is the tenth part of 100%.

Example 8.

Example 9.   How much is 20% of $80?  How much is 30%?  How much is 90%

Answer.   20% is twice as much as 10%.  Since 10% of $80 is $8, then 20% is 2 × $8 = $16.  30% is 3 × $8 = $24.  90% is 9 × $8 = $72.

See especially Problem 23 at the end of the Lesson.  And to see how to take 25% of a number, see Lesson 14.

To prepare for this next skill, can you name the powers of 10 backwards, starting with Million?

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Do it yourself first!

Million, hundred thousand, ten thousand, thousand, hundred, ten, one.

Example 10.   How much is 1% of One million?

Answer.   To take 1%, we must divide by 100.  But to do that, we can divide by 10 twice -- and that will take us two powers of 10 less:

Hundred thousand, Ten thousand.

Example 11.   How much is 6% of One million dollars?

Answer. Since 1% is Ten thousand dollars, then 6% is 6 times Ten thousand dollars, which is Sixty thousand dollars.

Example 12.   How much is 3% of Ninety thousand dollars?

Answer.   First, 1% is two powers of 10 less:  Nine hundred dollars. Therefore 3% is Twenty-seven hundred dollars.

Example 13.   How much is 8% of Three million dollars?

Answer.   Since 10% is Three hundred thousand dollars, then 8% is a bit less:  Two hundred forty thousand dollars.

Topics in percent continue in Lessons 14,  15,  16, and 27.

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Now, a percent is not a number.  Rather, it expresses a relationship between numbers. What percent -- what relationship --- has 6 to 12?
6 is 50% of 12.  That kind of relationship is called a ratio (Lesson 16), and understanding that percents are ratios will turn out to be extremely important.  To accomplish certain written calculations, however, it is necessary to represent a percent with a number.  And to that we now turn.

(This is often called changing a percent to a decimal.)

24% = .24     

Divide by 100 -- separate two decimal digits.  For, 24% -- 24 for each 100 -- means 24 hundredths.

Division by 100 is indicated by the percent sign itself  %, with its division slash / and two 0's.

Here are more examples:

Example 14.