Percentages, Ratio and Proportion Study Guide for McGraw-Hill's Firefighter Exams (page 3)

A percent is defined as one part in a hundred. The whole amount can be defined as 100 percent (%) and can be divided into 100 equal portions.

Converting Decimals to Percent and Vice Versa

To convert a decimal to a percent, move the decimal point two places to the right and insert the % sign at the end of your answer.

Example: 0.567 = 56.7%.

To convert a percent to a decimal, move the decimal point two places to the left, and remove the % sign at the end of your answer.

Example: 56.7% = 0.567.

Converting Fractions and Mixed Numbers to Percent and Vice Versa

To convert a fraction to a percent, multiply the fraction by 100%. Express the whole number (100) as a fraction by placing it over 1.

To convert a percent to a fraction, remember that the definition of percent is one part in a hundred. Remove the % sign and multiply the percent value by 1/100 and then reduce the fraction to its lowest terms.

To convert a mixed number percent to a fraction, eliminate the % sign and convert the mixed number to an improper fraction. Then, multiply the improper fraction by 1/100 to obtain the fraction.

Percent Problems—Finding the Part, Whole, or Percent

To find the part when given the whole and the percent, use the formula: Part = % · Whole ÷ 100

Example: What is 54% of 50?

Part = % · Whole ÷ 100

Part = (54) (50) ÷ 100

Part = 2700 ÷ 100 = 27

To find the % when given the whole and the part, use the formula: % = Part ÷ Whole · 100.

Example: What percent of 60 is 12?

% = (12) ÷ (60) · 100

% = 0.2 · 100

% = 20

To find the whole when given the part and %, use the formula: Whole = Part ÷ % · 100.

Example: 6 is 15% of what number?

Whole = Part ÷ % · 100

Whole = (6) ÷ (15) · 100

Whole = 0.4 · 100 = 40

Percent Problems—Increase and Decrease

Example: What is 60 increased by 10%?

Part = % · Whole ÷ 100

Part = (10) (60) ÷ 100

Part = 600 ÷ 100 = 6 Add the percentage increase to the original number.

60 + 6 = 66

Example: What is 12 decreased by 25%?

Part = % · Whole ÷ 100

Part = (25) (12) ÷ 100

Part = 300 ÷ 100 = 3 Subtract the percentage decrease from the original.

12 – 3 = 9