This page of our ParaPro study guide covers decimals. It explains what they are and how they are used. You will learn how to add, subtract, multiply, and divide them. We have also includes some examples that show how to solve these problems step-by-step. After reviewing all of this material, you can test your knowledge with our decimals review test.
What are Decimals?
Decimals are a way of representing numbers that fall between whole numbers. They are numbers that include a decimal point, which separates the whole part of the number from its fractional part.
For example, in the decimal number 3.14, “3” is the whole number part, and “14” is the fractional part. The decimal point separates the two parts.
With decimals, instead of the place values being labeled “ones,” “tens,” and “hundreds” etc. as in whole numbers, the places are named just a little different: “tenths,” “hundredths,” “thousandths,” and so on (there is no oneths place). In the example above, 3.14, 1 is in the tenths place and 4 is in the hundredths place.
Decimals are based on powers of 10. This means that a factor of ten will move a decimal point by one place:
$3.14 \times 10 = 31.4$
$3.14 ÷ 10 = .314$
Decimals are used extensively in mathematics, science, finance, and everyday life for expressing values that are not whole numbers, such as measurements, percentages, and monetary amounts.
Working with Decimals
To add or subtract decimal numbers, line up the decimals vertically and add/subtract. Use a 0 in place of any missing digits. The decimal point stays in the same location throughout.
Example 1
Add $.523+2.104$.
Example 2
Subtract $3.451-2.94201$.
To multiply decimals, line up numbers from the right, perform multiplication, and put back into your product however many digits after the original decimals in total.
Example 3
Multiply $(2.941)(3.51)$.
There are a total of five numbers after the decimal point in the original problem, so we move the decimal point 5 places in our product, 1032291.0 (the .0 is implied at the end of any whole number), to get the final answer of 10.32291.
To divide decimals, you can perform long division. If it is easier, you can move the decimal in both the number you are dividing by (the divisor) and in the number you are dividing into (the dividend). It is often easier to divide decimal numbers if you are able to convert the divisor into a whole number.
Example 4
Divide $13.2174÷2.1$.
$13.2174÷2.1$ is equivalent to $132.174÷21$
To compare the values of decimals, you can write all values with the decimals lined up. It is now easier to compare the values of the decimals because you can easily compare one place value at a time.
To convert a decimal to a fraction, you can put the decimal number over its place value. If necessary, simplify the resulting fraction. For example, .75 goes to the hundredths place, so its equivalent fraction would be $\frac{75}{100}$. That can be simplified to $\frac{3}{4}$.
Having reviewed all of this material, you should have a good idea of how decimals work. You should also know how to perform basic calculations with decimals. These are skills that will definitely be tested on the ParaPro assessment. As a final review, try the five review questions on the test below.