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A R I T H M E T I C

Lesson 3  Section 2

The Meaning of Percent

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

 7. What does "percent" mean? Percent is an abbreviation for the Latin per centum, which means for each 100.

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?

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

 8. How do we take 1% of a number? 1% of \$200 Divide it by 100.  For, 1% means 1 for each 100, which is the hundredth part.

1% = 1 for each 100.

Examples.

 1% of \$200 is \$2.00 Divide by 100:  Separate two decimal places. 1% of \$250 is \$2.50 Again, divide by 100:  Separate two decimal places. 1% of \$6.00 is \$.06 Move the point two places left.  Do not write the 0's that remain on the extreme right of the decimal: 6.00 ÷ 100 = .0600 = .06 (Lesson 2, Question 8.) 1% of \$1,200 is \$12.00 Divide by 100:  Separate two decimal places, or simply drop the two 0's.

Problem 1.   How much is 1% of \$400?  How much is 2% of \$400?  How much is 3%?  How much is 9%?

Answer.   1% of \$400 is \$4.00.   Separate two decimal places.

Now, 2% is twice as much as 1%.  Therefore 2% of \$400 is \$8.  3% is \$12.  4% would be \$16.  9%, therefore, is 9 × \$4 = \$36.

Problem 2.   How much is 8% of \$600?

Answer.   Since 1% is \$6.00, then 8% is 8 × \$6.00 = \$48.00.

Problem 3.   How much is 2% of \$325?  How much is 3%?  4%?

Answer.   We can get everything from 1%, which is \$3.25.

2%, therefore, is \$6.50.

3% is \$9.75.

And 4% is 4 × \$3.25 = 4 × \$3  +  4 × \$.25 = \$12 + \$1 = \$13.

These are problems that do not require a calculator. They should be done mentally!

 9. How do we take 10% of a number? 10% of \$600 Divide it by 10.  For, 10% means 10 for each 100. Each 10 is a tenth part of 100.

Examples.

 10% of \$600 is \$60. Divide by 10:  Take off one 0, or separate one decimal place. 10% of \$625 is \$62.50 Divide by 10.  Separate one decimal place:  \$62.5 But we write money with two decimal places (cents).  Therefore we must add a 0 onto the right. 10% of \$6.00 is \$.60 Move the point one place left.  Again, we write money with two decimal places.

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.

 10. How do we change a percent to a number? 24% = ? Divide by 100.

(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:

 .24% = .0024 Divide by 100:  Move the decimal point two places left. 9% = .09 Divide by 100:  Mark off two decimal places. 650% = 6.5 Divide by 100:  Mark off two decimal places. It is not necessary to write the 0 that remains on the right of the decimal.  650% = 6.50 = 6.5 6.5% = .065 Divide by 100:  Move the decimal point two places left.

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.

 11. How do we change a number to a percent? .24 =  ? % Multiply it by 100, and add the % sign.

Examples.

 .24  = 24% Multiply by 100:  Move the point two places right. 2.4  = 240% Move the point two places right. 24  = 2400% Multiply by 100:  Add on two 0's. .024  = 2.4% Move the point two places right.

Number to a Percent

.24 = 24%

Percent to a Number

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