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Decimals is a number system with a base number of 10 that can be used to express the numbers in between integers.
This is probably due to the fact that humans have ten digits on their hands.
We recognize decimals in everyday money transactions.
Cents are expressed with two decimal places or to the nearest hundredth.
It is also good to note that decimals are often required when dividing two numbers (like with a fraction)
½ is 1 ÷ 2 or 0 . 5
2 ⎮ 1 . 0 (here we add a decimal and a zero)
- 1 0
0
¼ is 1 ÷ 4 or 0 . 2 5
4 ⎮ 1 . 0 0 (here we add a decimal and as many zeros as necessary)
- 8
2 0
- 2 0
0
If the remainder of a division is not 0 then a more accurate answer can be found using decimals.
Reading and writing decimal numbers has four simple steps. (example: 1,234.567)
1) identify the whole number (one thousand two hundred thirty-four)
2) use the word "and" to represent the decimal point
3) identify the number to the right of the decimal point (five hundred sixty-seven)
4) identify the decimal placement of the last number (thousandths)
the final answer will read: one thousand two-hundred thirty-four and five hundred sixty-seven thousandths
This is a very old educational video from 1948 introducing the idea of using decimals.
Some of the terminology has changed over the last sixty years but the concepts in the video remain the same.
(this video is about two minutes)
When adding and subtracting with decimals, the same rules apply as with whole numbers.
The one thing to remember is to line up your decimal points in the equation (add zeros if need be)
Add or subtract normally and simply bring the decimal point down to the same position in the final answer
When multiplying with decimals use the same rules as with whole numbers.
The only difference is once you have your final product, add the number of decimal places within the numbers you multiplied
and put the decimal point in the number of places added (starting from the right-hand side).
When dividing with decimals before using the same rules as with whole numbers, you must first shift the decimal point over until it disappears and do the same shift to the number from which you are dividing.
Further hints...
Be careful when you first look at a decimal number. The numbers can be deceiving.
check out this fun video for a great decimal tip
(this video is under a minute)
ROUNDING
When rounding with decimals the same rules apply as with rounding with whole numbers.
Look to the right of the decimal place you are rounding off to.
If it's a five or more round up. If it's a four or less change nothing.
Please note: unlike with whole numbers there is no nearest 'one' place.
The first number after the decimal point is the tenth spot, then the hundredth,
then the thousandth, then ten-thousandth and so on.
MULTIPLYING and DIVIDING with 10, 100, 1 000 ...
When multiplying and dividing by 10, 100, 1 000 and so on ...
we can move the decimal either left or right the desired number of spaces.
3 x 10 = 30 4.356 x 100 = 435.6 60 000 ÷ 1 000 = 60
3.1 x 10 = 31 586.93 ÷ 100 = 5.8693 58.123 x 10 = 581.23
ONLINE TESTS
Test your skills adding, subtracting, multiplying, dividing and rounding decimals at
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/decimals/usingdecimals/quiz.shtml
(there are three levels of difficulty to choose from)
Test your skills multiplying and dividing with 10, 100, and 1 000 at
Test your skills comparing fractions to decimals at
(there are three levels of difficulty to choose from)
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