PRESENTATION 2Percents

PERCENTS

•Indicates number of hundredths in a whole

•A decimal fraction can be expressed as a percent by moving the decimal point two places to the right and inserting the percent symbol

ESTIMATING

•Example: Express 0.0152 as a percent:

•Move decimal point two places to right

0.0152 = 1.52

•Insert percent symbol

0.0152 = 1.52%

FRACTIONS TO PERCENTS•To express a common fraction as a percent:

•First, express the fraction as a decimal by dividing the numerator by the denominator

•Convert the answer to a percent by moving the decimal point two places to the right

FRACTIONS TO PERCENTS•Example: Express as a percent:

•First convert the fraction to a decimal by dividing

•Then change the decimal to a percent

0.875 = 87.5%

78

0.8758 7.000

6460564040

PERCENTS TO FRACTIONS

•To express percent as decimal fraction:

•Drop the percent symbol

•Move decimal point two places to the left

PERCENTS TO FRACTIONS•Example: Express as a decimal and round the

answer to 4 decimal places

•Convert the fraction to 0.76

•Drop the percent symbol and move the decimal point 2 places to the left:

38.76% = 0.3876

PERCENTS TO FRACTIONS

•To express a percent as a common fraction:

•First convert percent to a decimal fraction

•Then express the decimal fraction as a common fraction

PERCENTS TO FRACTIONS

•Example: Express 37.5% as a common fraction

•Express 37.5% as a decimal

•Express 0.375 as a common fraction37.5% 0.375

PERCENT TERMS DEFINED

•All simple percent problems have three parts:

• Rate is the percent (%)

• Base represents whole or quantity equal to 100%

• Word “of” generally relates to the base

• Percentage is part or quantity of percent of the base

• Word “is” generally relates to the percentage

PERCENT TERMS DEFINED

•Example: Identify base, rate, and percentage

What percent of 48 is 12?

•Problem is asking for rate (percent)

•The number 48 represents whole and is identified by word “of,” so it is the base

•The number 12 represents part and is identified by word “is,” so it is the percentage

FINDING THE PERCENTAGE•Proportion formula for all three types of

percentage problems:

•Where:• B is the base

• P is the percentage or part of the base

• R is the rate or percent

100

P RB

FINDING THE PERCENTAGE•Example: What is 15% of 60?

•The base, B, is 60: the number of which the rate is taken—the whole or a quantity equal to 100%

•The problem is asking for the percentage (part): the quantity of the percent of the base

FINDING THE PERCENTAGE

•The proportion is:

•Use cross-products and division:

1560 100P

100 15 60

100 900

900100

P

P

P

FINDING THE RATE

•Example: What percent of 12.87 is 9.62 rounded to 1 decimal place?

•The base, B, or whole quantity equal to 100% is 12.87

•The percentage, P, or quantity of the percent of the base is 9.620

•The rate, R, is to be found

FINDING THE RATE

•The proportion is:

•Cross multiply:

•Divide:

9.62012.87 100

R

9.620 100 12.87

962 12.87

R

R

FINDING THE BASE•Example: 816 is 68% of what number?

•The rate, R, is 68%

•The percentage, P, is 816

•The base, B, is to be found

•The proportion is:

•Solve for B:816 68

100B

PRACTICAL PROBLEMS

•A 22-liter capacity radiator requires 6.5 liters of antifreeze to give protection to -17ºC.

•What percent of the coolant is antifreeze? Round the answer to the nearest whole percent.

PRACTICAL PROBLEMS

•In this problem: •The percentage (P) or the part is 6.5

liters•The base (B) is 22 liters•The rate (R) or percent is unknown•Set up the formula and solve

PRACTICAL PROBLEMS•Solve:

•The antifreeze is 30% of the coolant