134 CHAPTER 2 Linear Equations and Inequalities in One Variable

Basic percent

equation

Converting Between Decimals and Percents

(a)Write 75% as a decimal.

The fraction form can also be used to convert 75% to a decimal.

(b)Write 3% as a decimal.

(c) Write 0.375 as a percent.

(d)Write 2.63 as a percent.

NOW TRY

We can solve a percent problem involving x% by writing it as the proportion

The amount, or percentage,is compared to the base(the whole amount). Another

way to write this proportion is

Solving Percent Equations

Solve each problem.

(a)What is 15% of 600?

Let n the number. The word ofindicates multiplication.

What is 15% of 600?

n 0.15 600 Write the percent equation.

Multiply.

Thus, 90 is 15% of 600.

(b)32% of what number is 64?

32% of what number is 64?

0.32 n 64 Write the percent equation.

Divide by 0.32.

Simplify. Use a calculator.

32% of 200 is 64.

n= 200

n=

64

0.32

=

n= 90

= #

=

EXAMPLE 8

amountpercent (as a decimal)#base.

amount

base

=percent (as a decimal )

amount

base



x

100

.

2.63= 263 #0.01= 263 #1%=263%

0.375=37.5#0.01= 37.5#1%= 37.5%

3%= 3 #1%= 3 #0.01=0.03

75%= 75 #1%= 75 #

1

100

=

75

100

= 0.75

1%=

1

100

75%= 75 #1%= 75 #0.01= 0.75

EXAMPLE 7

Write 32%

as a decimal.

Write 15% as

a decimal.

Translate each word or

phrase to write the equation.

NOW TRY
EXERCISE 7
Convert.

(a)16% to a decimal

(b)1.5 to a percent

NOW TRY ANSWERS

7. (a)0.16 (b)150%

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