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Decimal Worksheets

Click on the Decimal worksheet set you wish to view below.

  1. Compare and Order Decimals, Percents and Fractions
  2. Converting Percentages to Fractions and Decimals
  3. Decimal Addition (Thousandths)
  4. Decimal Division (Hundredths)
  5. Decimal Multiplication (Hundredths)
  6. Decimal Subtraction (Thousandths)
  7. Decimal Word Problems
  8. Decimals to Fractions and Percentages
  9. Fractions to Decimals and Percentages
  10. Rounding to Tens Place
  11. Visualizing Decimals

Decimal Worksheet Makers

  1. Basic Math Worksheet Maker
  2. Basic Operation Math Quiz Maker
  3. Decimals/Fractions
  4. Decimals - Area Models

What are decimals?

The word refers to a number system that uses ten symbols (deci means ten). It also means writing fractions with the same system. For instance, one fourth can be written as 1/4 or 0.25 - the second representation is from the decimal system (using a decimal point).

While it may seem obvious that counting uses the digits 0,1,2,3,4,5,6,7,8, and 9, this wasn't always the system used. Even today, computers use a system based on just 0 and 1 - the binary system.

A basic problem in decimals.

One problem that comes up when using decimal notation is how to write a fraction that doesn't divide evenly by a multiple of ten. (Remember, decimals are based on tenths, hundreds, thousandths and so on.) If you try to write 1/3 as a decimal, you will get a series of 3's that never ends. To solve this problem, 1/3 (and any other fraction that doesn't divide evenly) is written with three dots at the end: 0.333... The "..." means that the string of digits goes on forever.

How are decimals used in the real world?

If you've ever tried to add fractions, like 1/8 plus 4/5, you know there can be considerable effort involved. You have to convert one or the other fraction (or both) so that their denominators (the lower number) match up. Decimals all use multiples of 10 for the denominator (one tenth, one one-hundredth and so on).

So the problem, 1/8 + 4/5 would look like this in decimals: 0.125 + 0.8 and the two decimals can be added directly to get 0.925. Because addition, multiplication and other mathematical operations are easier with decimals, they are used throughout scientific and engineering work.

Who invented decimals?

One person didn't invent the decimal system. Rather, it evolved over a long, long time and had other competitors. For instance, The Babylonian system (which is based on multiples of 6's - 12, 36 and so on) is still around in the form of the number of minutes in an hour, the number of seconds in a minute, and the number of degrees (360) in a circle.

What is known is that the decimal system gained wide use and acceptance by way of Indian mathematicians during the 9th century. Parts of it were in use earlier in Asia and the Middle East, but it spread from India in the form we use today.

Decimal fractions were written about in the 10th century by the Arabic mathematician Al-Uqlidisi, and he showed how to convert regular fractions into decimal form.

An interesting fact about decimals.

The decimal system has an interesting 'flaw'. In some cases, the same quantity can be written in two different ways.

For instance, the number 1 is the same as 0.999... I mean it is the same exactly. The two ways of writing it mean the same thing.

You can prove it this way:

Take 0.999... and multiply it by 10 to get 9.999...

Now, subtract 0.999... from this to get 9 Since we started with 10 times the number and subtracted the starting number once, our answer ( 9 ) must be 9 times the original number. Of course, 9 is 9 X 1 and our original number must be equal to 1.

10X - X = 9X and 9X / 9 = X

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