To understand the % sign, ask yourself the following four questions:

(1) What does the % sign mean?

. . .  A % is used to compare a number (any number) to 100 using division.

Under normal circumstances, all numbers are compared to the number 1 using division.

For example, the number 3 is only a 3 when it is compared to the number 1 using division. It is three times as big as the number 1.

However, a % does not use the number 1 for comparison purposes.

A % is used to compare a number (any number) to 100 using division.

Continuing on with the number 3 compared to the number 1 as an example, the result is: (Note that the quotient must still equal 3. The number 300 is three times as big as 100.)

The final percentage is:

3 = 300%

. . .  Any Number can be converted to a percent

You can complete a short calculation similar to the example shown above, or . . .

. . . Just move the decimal point to the right by two places.

(2) Where is a % symbol used?

. . .  A % symbol is only used to represent a proportion.

A percent tells you that you are dealing with a ratio , or relative comparison (using division).

Although any number can be converted into a %, percents are only used to represent ratios (proportions).

. . .  What is the point of converting a ratio to a % ?

Is there any advantage to saying 5.6% instead of .056?

Read on . . .

(3) How is a % symbol used in everyday life?

. . .  There are thousands and thousands of applications where the concept of a percent is used every day.

The fact that a percent represents a proportion (a relative comparison) is what makes valuable.

Here are some common examples :

. . .  Sales Tax . . .

When you pay a sales tax, the tax rate will be stated as a % .

If the sales tax rate is 8%, this means that you will pay the government a tax of 8 dollars for every 100 dollars you spend.

If you spend $100, you owe a tax of $8. If you spend $200, you owe tax of $16. If you spend $50, you owe a tax of $4. If you spend $25, you owe a tax of $2, and so on. The sales tax you owe is always the same proportion of what you spend (in these examples it is 8% of what you spend).

. . .  Bank Interest . . .

If you deposit money in a bank, the interest the bank will pay on your account will be stated as a % .

If the interest rate is 5% (simple annual interest), this means that the bank will pay you 5 dollars for every $100 you leave in your account for one year.

If you leave a $100 deposit in the bank for two years, you will receive $10 ($5 per year). If you leave a $100 deposit in the bank for only six months, you will receive $2.50, and so on. The amount your deposit earns is always the same proportion.

. . .  Credit Card Interest . . .

If you use a credit card, the interest you pay on the outstanding balance you owe will be stated as a % .

If the interest rate is 20% (simple annual interest), this means that you pay the credit card company an extra 20 dollars per year for every $100 of unpaid debt.

. . .  Test Grades in School . . .

Test grades in school are often stated as a % .

If a student has a test average of 81%, this means that for every 100 questions the student answers on his or her tests, 81 questions are answered correctly.

. . .  Slope of a railroad track . . .

Slope (the incline of the tracks) is often stated as a % .

If a slope of a railroad track is a 5% grade, this means that for every 100 feet of horizontal distance the tracks drop (or increase) 5 feet in elevation.

. . .  Survey (Poll) . . .

Survey results are often stated as a % .

If a survey found that 75% of restaurant patrons preferred a certain type of food, this means that for every 100 people, 75 people prefer that type of food.

(4) What math symbols can be mistaken for a % sign ?

. . .  Per mille . . .

. . .  The Per mille symbol is not equivalent to a Percent symbol.

1 % (percent) means 1 part in 100.

1 (per mille) means 1 part in 1000.

. . .  Basis point . . .

. . .  The Basis point symbol is not equivalent to a Percent symbol.

1 % (percent) means 1 part in 100.

1 (basis point) means 1 part in 10,000.