All About Decimals

1. What are decimals?

Decimals are numbers that can be expressed as fractions, where the denominators are powers of ten.

Decimals come into play when you go right of the decimal place. When you do so, you are dealing with numbers that are less than one and that are equal to numbers where the denominator is either 10, 100, 1000 and so on, because decimals can be written as fractions.

Fractions and decimals go hand-in-hand. 0.1 = 1/10; 0.01 = 1/100 and 0.001 = 1/1000.

2. How to Read Decimals

To the left of the decimal point, the numbers are equal or greater than one (zero can also be represented) and to the right of the decimal point the numbers are less than one (expressed as powers of ten in the denominator, if they were written as fractions).

You read decimals as reading the numbers to the left, as normal, and the numbers to the right while saying their place value. So:

15.34 is fifteen and 34 hundredths

3. Adding and Subtracting Decimals

Line up the decimals: Make sure the numbers are lined up by their decimal points. This way, all the digits are in the correct columns (like the ones, tenths, hundredths, etc.).

Add or subtract like normal: Just add or subtract the numbers like you would with whole numbers.

Bring the decimal down: After adding or subtracting, just bring the decimal point straight down into your answer.

Example:
3.25  

+1.70  

4.95

4. Multiplying Decimals

Advance to 3:30, in the video, to pick up with multiplying decimals.

Ignore the decimals first: Multiply the numbers as if they were whole numbers, without worrying about the decimal points.

Count the decimal places: Count the total number of decimal places in both numbers. This tells you how many decimal places the answer should have.

Place the decimal: In your answer, move the decimal point to the left by the number of places you counted.

Word Problem

Additional Multiplication of Decimals Example:

Another Example:

2.5 

× 0.4

 1 0 0  =   1.00   (2 decimal places total, so 1.00 or just 1)

5. Dividing Decimals

Advance to 5:06, in the video, to pick up with dividing decimals.

Move the decimal: If you’re dividing by a decimal, move the decimal point in the divisor (the number you’re dividing by) to the right until it’s a whole number. Do the same thing to the dividend (the number being divided), by the same number of spaces.

Divide like normal: Now, divide the numbers as if they were whole numbers.

Place the decimal: Put the decimal point in the answer directly above where it is in the dividend.

Here’s another example:

6.4 ÷ 0.8 = 8.0 (Move decimal in both numbers, then divide)