Basic Terms and Terminology Relating to Solving Problems Involving Percentages

  • Percentages are a number with a % sign that represent numbers in comparison to 100.

Percentages and Their Meaning

Pie Chart

Percentages are a number with a % sign that represent numbers in comparison to 100. As shown in the picture below, of all of the persons using a web browser to access Wikipedia, 20.03 %, or 20.03 people out of every hundred people, used Chrome and 19.26% of all of the persons using a web browser to access Wikipedia, 19.26%, or 19.26 people out of every hundred people, used Firefox, etc.

100% is the whole and it is equal to 1. Percentages less than 100% are less than 1 or the whole and percentages more than 100% are more than one or the whole; and percentages less than 1% are also possible.

Some examples of percentages less than 100% that are less than 1 and less than the whole are:

  • 16%
  • 25%
  • 76%
  • 89%
  • 99%

Some examples of percentages more than 100% that are more than 1 and more than the whole are:

  • 123%
  • 167%
  • 200%
  • 399%
  • 546%

Some examples of percentages less than 1% that are less than the whole AND less than 1 out of every hundred are:

  • 3/4%
  • 1/25%
  • 007%
  • 1%
  • 009%

Converting Among Fractions, Decimals, Ratios and Percentages

Percentages have equivalents in terms of a fraction, a decimal point number and as a ratio.

You may have noticed a pattern in the chart above suggesting how to convert among fractions, decimals and percentages.

The conversion of percentages into fractions is done by simply placing the percentage number over 100. Regardless of whether or not the percentage number is less than or greater than 100, the denominator of the fraction is always 100

Here are some examples:

  • 12% = 12/100
  • 120% = 120/100
  • 220% = 220/100
  • 2222% = 2222/100

The conversion of percentages into decimal numbers is done by moving the percentage number's decimal place 2 places to the left. As previously discussed, dividing by 100 can be done simply by moving the decimal place two places to the left.

Here are some examples:

  • 12% = 0.12
  • 120% = 1.20
  • 220% = 2.20
  • 2222% = 22

The conversion of percentages into ratios is done by placing the percentage number and then : (colon) and then 100. A ratio is read as 12 is to 100 when you see 12 : 100. There are 12 per hundred.

Here are some examples:

  • 12% = 12 : 100
  • 120% = 120 : 100
  • 220% = 220 : 100
  • 2222% = 2222 : 100

Calculating Problems Involving Percentages

In your everyday life, you use and calculate with percentages more than you think.

Here are some of the everyday percentages that you use on a daily or regular basis:

  • BOGO or Buy 1 and Get 1 Free
  • 30% off men's shirts
  • Your weight goal is to lose 5% of your weight every 6 months
  • You financial goal is to save 3% of your annual salary each year

Example 1: Calculating Problems Involving Percentages

Your local grocery store is having a huge BOGO sale this week. You will be purchasing 1 of each of these BOGO items this week and your store does NOT require that you take 2 to get the BOGO discount:

Cereal (usual price is $5.39 per box)

50% of $5.39

1/2 x $5.39 OR 0.5 x $5.39 OR 50% : !00% = x : $5.39

1/2 x $5.39 = $5.29/2 = $2.70 rounded off to the nearest penny

OR

0.5 x $5.39 = $2.70 rounded off to the nearest penny

OR

50% : !00% = x : $5.39

50/100 = x / $5.39

x=$2.70 rounded off to the nearest penny

In this example, you have paid $2.70 per box of cereal and you have also saved $2.69 per box of cereal.

Example 2: Calculating Problems Involving Percentages

You will be purchasing each of these shirts during the 30% off sale. How much will you save with the purchase of these 4 shirts?

  • Blue shirt (Regular price is $19.99)

When shirts are discounted by 30%, you will be paying only 70% of the regular price for the shirt. So, in order to find out what you are saving per shirt, you would have to calculate 30% of the regular price; and, in order to determine what you will be spending for each discounted shirt, you would have to calculate 70% of the regular price.

1/3 x $19.99 OR 0.33 x $19.99 OR 30% : 100% = x : $19.99

1/3 x $19.99 = $19.99/3 = $6.66 rounded off to the nearest penny

OR

0.33 x $19.99 = $6.66 rounder off the nearest penny

OR

30% : 100% = x : $19.99

30/100 = x / $19.99

x = $6.66 rounded off to the nearest penny

In this example, you have saved $6.66 for this blue shirt.

Example 3: Calculating Problems Involving Percentages

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

  • Your weight: 160 pounds

5/100 x 160 pounds OR 0.05 x 160 pounds OR 5% : 100% = x : 160 pounds

5 /100 OR 1/20 x 160 pounds = 8 pounds

OR

0.05 x 160 pounds = 8 pounds

OR

5% : 100% = x : 160 pounds

5/100 = x/160

x = 8 pounds

In this example, you should lose 8 pounds every 6 months.

Example 4: Calculating Problems Involving Percentages

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

  • Your weight: 65 kilograms

5/100 x 65 kg OR 0.05 x 65 kg OR 5% : 100% = x : 65 kg

5/100 OR 1/20 x 65 kg = 3.25 kg

OR

0.05 x 65 kg = 3.25 kg

OR

5% : 100% = x : 65 kg

5/100 = x/65

x = 3.25 kg

In this example, you should lose 3.25 kg every 6 months.

Example 5: Calculating Problems Involving Percentages

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

  • Your weight: 89 kilograms

5/100 x 89 kg OR 0.05 x 89 kg OR 5% : 100% = x : 89 kg

5/100 OR 1/20 x 89 kg = 4.45 kg

OR

0.05 x 89 kg = 4.45 kg

OR

5% : 100% = x : 89 kg

5/100 = x/89

x = 4.45 kg

In this example, you should lose 4.45 kg every 6 months.

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Alene Burke

Alene Burke

Alene Burke RN, MSN is a nationally recognized nursing educator. She began her work career as an elementary school teacher in New York City and later attended Queensborough Community College for her associate degree in nursing. She worked as a registered nurse in the critical care area of a local community hospital and, at this time, she was committed to become a nursing educator. She got her bachelor’s of science in nursing with Excelsior College, a part of the New York State University and immediately upon graduation she began graduate school at Adelphi University on Long Island, New York. She graduated Summa Cum Laude from Adelphi with a double masters degree in both Nursing Education and Nursing Administration and immediately began the PhD in nursing coursework at the same university. She has authored hundreds of courses for healthcare professionals including nurses, she serves as a nurse consultant for healthcare facilities and private corporations, she is also an approved provider of continuing education for nurses and other disciplines and has also served as a member of the American Nurses Association’s task force on competency and education for the nursing team members.
Alene Burke

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