Workplace Math and PLAR Prep

Decimals

Decimals allow you to work with parts of numbers.

Decimals have different place values. They are places to the right of the decimal point.

You have been working with decimals for a long time. In money, any amount less than a dollar is a decimal.

Reading Decimals

The dot in the decimal is called the decimal point.
It is written to the right of the ones place.
The first place to the right after the decimal point is the tenths place.
Place value continues on both sides of the decimal point

The number written under the chart is 65,218.3479.

It is read “sixty-five thousand, two hundred eighteen and three thousand four hundred seventy-nine thousandths.”
The comma helps you read whole numbers by marking off the periods (thousands, millions, billions).
The decimal point is different. It shows you where the whole number ends and the decimal number begins.
The decimal point does not take up a place. Only a number can take up a place.
Any decimal no matter how large is less than the whole number 1.
Any number that has both a whole number and a decimal number in it is larger than a number that has a decimal only.

Comparing Decimals

If there are no whole numbers, or if the whole numbers are the same, you have to compare the decimal number.

Here is a trick you can use to compare decimals.

For example: Which is larger? 0.07 or 0.2?

1. Add one zero at the end of 0.2 – by adding the zero, you have 0.07 and 0.20

2. Compare: 20 hundredths is larger than 7 hundredths

3. The answer is 0.2

Let’s try this one: Arrange the following decimals in order from the smallest to the largest: 0.8, 0.08, 0.088, 0.808.

1. Add zeros so each decimal has three places. .800, .080, .088, .808

2. Compare and arrange the decimals in the correct order: .080, .088, .800, .808

3. Leave the zeros out in the final answer. .08, .088, .8, .808.

Adding Decimals

Decimals are added the same way whole numbers are added.

To add decimals, line up the decimal points and add as you would whole numbers.

For example: Add 24.29 + 12.95.

Write the question so the decimal points are lined up.
Add the hundredths.
Add the tenths.
Add the whole numbers.
Line up the decimal points.

Subtracting Decimals

Decimals are subtracted the same way whole numbers are subtracted.

You just have to make sure the decimal points are lined up.

For example: Subtract 7.2 − 3.7

Write the question so the decimal points are lined up.
Subtract the tenths.
Subtract the whole numbers.
Line up the decimal points.

Multiplying Decimals

To multiply decimals, multiply the same way you would multiply whole numbers, except you must put the decimal point in. Count the number of decimal places in both numbers you are multiplying and put the total number of places in your answer.

For example: Multiply 4.8 x 0.9

Arrange in columns and multiply.
Place the decimal point in the answer so that the number of places in the answer is the same as the two numbers that were multiplied.

Multiplying Decimals by 10, 100, and 1000

There are shortcuts when multiplying decimals by 10, 100 and 1000.

Move the decimal point one place to the right when you multiply by 10. 0.34 x 10 = 3.4
Move the decimal point two places to the right when you multiply by 100. 0.34 x 100 = 34
Move the decimal point three places to the right when you multiply by 1000. 0.34 x1000 = 340 Notice the pattern for multiplying a number by 0.1, 0.01, or 0.001.
Move the decimal point one place to the left when you multiply by 0.1. 637 x 0.1 = 63.7
Move the decimal point two places to the left when you multiply by 0.01. 637 x 0.01 = 6.37
Move the decimal point three places to the left when you multiply by 0.001. 637 x 0.001 = .637