Converting Decimals and Percents

1. Converting a Decimal Into a Percent

Before we can convert between decimals and percentages, we need to discuss what a percentage is. A percent or percentage is a number that relates a part to the whole, where the whole is always 100. The word percent literally means “per 100.” 50%, then, means 50 per every 100. Percentages can be expressed in percent form, decimal form, and fraction form. The symbol % means percent in the percentage form of a number.

Almost all items, such as ingredients in a recipe, temperatures, grades, salaries, and distances, are presented as either a fraction, a decimal, or a percentage. In order to make comparisons or draw conclusions that you can apply to meet an objective, you will need to know how to make conversions.

To convert any number into a percent, multiply it by 100.

EXAMPLE

Convert 0.45 into a percent.

	The decimal
	Multiply the values without decimals: 45 times 100.
	Because there are two total decimal places in the multiplied values, move the decimal two places from the right in your answer.
	The decimal 0.45 can be written as 45%.

EXAMPLE

Convert 2.435 into a percent.

	The decimal
	Multiply the values without decimals: 2435 times 100.
	Because there are three total decimal places in the multiplied values, move the decimal three places from the right in your answer.
	The decimal 2.435 can be written as 243.5%.

hint

When multiplying by 100, there is a shortcut you can take. As we have discussed earlier, “100” is two decimal places because it is two powers of 10. Because we know this, instead of going through long multiplication, just move the decimal point two places to the right. Look back at the two examples we’ve just completed. In all cases, the end answer just had the decimal place moved to the right twice—regardless of where the decimal place started.

try it

Consider the decimals in the table below.

Decimal	Percent
0.25	?
0.17	?
0.3	?
0.01	?

Convert the decimals into a percent.

Decimal	Percent
0.25	25%
0.17	17%
0.3	30%
0.01	1%

You'll notice that for 0.3, when you move the decimal over two spots, you needed to fill in an empty space with a zero to make it 30%, not just 3%.

term to know

Percentage

A number that relates a part to the whole, where the whole is always 100.

2. Converting a Percent Into a Decimal

To convert a percent into a decimal, you do the opposite function and divide by 100. Remember, because a percent is “parts of a 100,” this means you divide by 100. You can also do the reverse of the shortcut from above. When converting a percent to a decimal, you can move the decimal point two places to the left.

EXAMPLE

Convert 50% into a decimal.

	The percent
	We can use our “move the decimal point” trick again, but in this case, since we are now dividing, you need to move the decimal point two places to the left instead of the right.
	The percent 50% can be written as 0.50.

EXAMPLE

Convert 372% into a decimal.

	The percent
	Using our decimal point trick again, move the decimal point two places to the left.
3.72	The percent 372% can be written as 3.72.

try it

Convert each of the following percents into a decimal.

Write 83% as a decimal.

	The percent
	Divide by 100 by moving the decimal point two places to the left.
	83% can be written as 0.83.

Write 4.5% as a decimal.

	The percent
	Divide by 100 by moving the decimal point two places to the left.
	4.5% can be written as 0.045.

hint

Don’t like converting percentages into a decimal? You can think of percentages as fractions as well. In the fraction form of a percent, 100 is the denominator. For example, 75% could be written as 75/100. From here, you can simplify the fraction to become ¾ and then convert it to a decimal.