PRESENTATION 2 Percents PERCENTS Indicates number of hundredths

PRESENTATION 2 Percents

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%

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 fraction

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

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:

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:

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:

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