There are many problems that arise every day involving the percent expression. The greatest number of percentage problems involve some kind of comparison of a part to the whole. Such comparisons become percentage problems when the ratio fraction is expressed as a percent.

A fraction having the specific power of 100 for the denominator is given the name percent. When writing these fractions, the percent symbol (%) is substituted for the denominator. Any common fraction or decimal can be expressed as a percent. The fraction 1/5 can thus be expressed as 0.20 or as 20 percent or simply as 20%. Note that the percent is the same as the decimal fraction except that the decimal point has been moved two places to the right and deleted after "percent" or the symbol "%" has been added.

Expressing a Decimal as a Percent

To express a decimal as a percent, move the decimal point two places to the right (add a zero if necessary) and affix the percent symbol.

EXAMPLE

Express 0.90 as a percent.

FIRST: Move the decimal point two places to the right.

90.

NEXT: Affix the percent symbol to the right after dropping the decimal point.

90%

Expressing a Percent as a Decimal

Sometimes it may be necessary to express a percent as a decimal. Keeping in mind that a percent is simply a decimal with the decimal point moved two places to the right, all that is necessary to express a percent as a decimal is to move the decimal point two places to the left.

Expressing a Common Fraction as a Percent

The technique involved in expressing a common fraction as a percent is essentially the same as that for a decimal fraction. The one difference is the procedure necessary to convert the fraction to a decimal.

EXAMPLE

Express 5/8 as a percent.

FIRST: Convert the fraction to a decimal.

**5**
**--- = 5 divided by 8 = 0.625**
**8**

NEXT: Move the decimal point two places to the right and affix the percent symbol.

0.625 = 62.5%

Finding What Percent One Number is of Another

Determining what percent one number is of another is done by writing the part number as the numerator of a fraction and the whole number as the denominator of that fraction, and expressing this fraction as percentage.

EXAMPLE

A motor rated as 12 horsepower is found to be delivering 10.75 horsepower. What is the motor efficiency expressed in percent?

FIRST: Write the part number, 10.75, as the numerator of a fraction whose denominator is the whole number, 12.

**10.75**
**-----**
**12**

NEXT: Convert the fraction to its decimal equivalent.

10.75 divided by 12 = 0.8958

THEN: Express the decimal as a percent.

0.8958 = 89.58% efficient.

Finding a Percent of a Given Number

The technique used in determining a percent of a given number is based on the fundamental process of multiplication. It is necessary to state the desired percent as a decimal or common fraction and multiply the given number by the percent expressed as a decimal or other fraction.

EXAMPLE

The cruising speed of an airplane at an altitude of 7,500 feet is 290 knots. What is the cruising speed at 9,000 feet if it has increased 6 percent?

FIRST: State the desired percent as a decimal.

6% = 0.06

NEXT: Multiply the given number by the decimal expression.

290 x 0.06 = 17.40

THEN: Add the new product to the given number. This is the new cruising speed.

290 + 17.4 = 307.4 knots.

Finding a Number When a Percent of it is Known

To determine a number when a percent of it is known, express the percent as a decimal and divide the known number by the decimal expression.

EXAMPLE

Eighty ohms represent 52 percent of a circuit's total resistance. Find the total resistance of this circuit.

FIRST: Express the percent as a decimal.

52% = 0.52

NEXT: Divide the known number by the decimal expression.

80 divided by 0.52 = 153.8 ohms total resistance.