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 all of 12.

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

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

What percent of the squares have been shaded?

Answer.   32% -- 32 for each 100.

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 for each 30 is equivalent to 100 for each 100.)

1% = 1 for each 100.

Examples.

Examples.

Problem.   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.

The meaning of percent continues in Lesson 14 and Lesson 27.

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

24% = .24     

Divide by 100 -- separate two decimal places.  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:

Strictly, a percent is not a number, it is a ratio (Lesson 27). Therefore we should speak rather of a number representing a percent. That becomes necessary only for certain written calculations.

Examples.