Percent

The use of percent is commonplace, not only in calculating tips, tax, and loan interest, but also in everyday language. When someone says he gave 100 percent or 110 percent, what does he mean? Whether he realizes it or not, he is referring to the definition of percent.

Percent means "parts per one hundred," and is designated by the % symbol. Thus, 100% is equivalent to , which is why 100% in common language can be interpreted as "totally," "completely," and "without any left behind." So, 110% is equivalent to , which is why in everyday language, 110% means to go above and beyond.

Conversions between Percents, Fractions, and Decimals

Since a percent is parts per one hundred, converting percent to a fraction is the easiest conversion. Just remove the percent symbol, place the number over one hundred, and reduce, as shown in the first (left-most) portion of the table.

To convert a percent to a decimal, start the same way. Remove the percent symbol and place the number over one hundred. Since a fraction represents division, divide the number by one hundred to get decimal form. (This is the same as moving the decimal to the left two places.) See the second part of the table.

To go in the opposite direction and convert decimal to percent, do the opposite operation. Multiply by one hundred. This is the same as moving the decimal to the right two places. See the third part of the table.

Converting a fraction to a percent can sometimes be done in one step but may require two steps. To convert in one step, multiply the fraction by some number to get parts per one hundred. If parts per one hundred cannot be easily obtained, convert the fraction to a decimal (by dividing), and then convert the decimal to a percent (by multiplying by 100). See the fourth (right-most) portion of the table.

EXAMPLES OF CONVERSIONS
Percent to Fraction		Percent to Decimal		Decimal to Percent		Fraction to Percent
Percent	Fraction	Percent	Decimal	Decimal	Percent	Fraction	Percent
45		60		0.23	0.23 × 100 = 23
220		115		0.8	0.8 × 100 = 80
		3		5.25	5.25 × 100 = 525	1¼
							2 ÷ 22 = 0.090909...≈9

Solving Percent Word Problems

There are at least two methods for solving percent word problems. One is to set up a proportion with percent over one hundred equal to parts out of the whole. Another way is to write an equation by translating English into algebra. Most commonly, "of" means multiply and "is" means equals. Both methods work, and the preferred method depends on the individual's strengths. See the sample problems in the table below.

Smart Shopping

Understanding percent is especially important in planning large purchases. The formula for simple interest is I = prt, in which I is the amount of

interest, p is the principal (the initial amount) , r is the interest rate, and t is time in years.

Suppose Susan is planning to finance a $20,000 automobile over 4 years. The lender offers her an interest rate of 8%, and she takes it. Using the simple interest formula, the interest paid out over the 4 years is I = 20,000 × 0.08 × 4 = $6,400.

Notice that Susan would have saved $6,400 if she had paid cash for the car. In addition to saving $6,400, that $6,400 could have been earning interest in a savings account. If the $6,400 had been placed in a savings account earning 2% interest over those same 4 years, the interest she would have earned is I = 6,400 × 0.02 × 4 = $512. In those 4 years, she could have saved $6,400 + $512 = $6,912!

Unfortunately, for many people it is difficult to save $20,000. Three ways Susan could have gotten a loan but still saved money are by (1) putting down a down payment, (2) shopping around for a loan with a lower interest rate, and (3) paying off the loan in less time.

Suppose Susan had put down $5,000 on the car and had taken out a loan for only $15,000. If she had shopped around to find an interest rate of7.25% and had agreed to pay off the loan in 3 years, the amount of interest paid over the 3 years would have been I = 15,000 × 0.0725 × 3 = $3,262.50.

By putting down a down payment, finding a lower interest rate, and paying the car off sooner, she would have saved over $3,000. Furthermore, she could have earned interest on the $3,000, making the savings even more.