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Decimals

Here are a couple of questions to help get us thinking along the right track:

  1. Why is it useful to be able to write fractions as decimals and vice versa?
  2. If working with decimals is easier than working with fractions, then why even bother working with fractions at all?

Take a coffee-talk coffee break!Take a few moments to think about these. Post an idea or response regarding this topic to the Discussion Forum entitled: Critical Thinking Questions.

Welcome back. (Well, hopefully you've been to the discussion forum and done a little critical thinking about math.) It might feel a bit unusual at first, but it's a good idea to think about math ideas independently at times so that you'll be able to take a more active role in your learning. Why? The biggest reason is that you'll be able to remember concepts and ideas that you make your own. When you learn a new concept, try paraphrasing these ideas into your own words. Try to put yourself in the place of the person who originally discovered the concept in the first place. It is much more exciting & engaging to discover something new than to merely learn something that someone else discovered or invented many many years ago. Try to make these concepts new! Make them your own, and then you will truly own them, --and you won't forget them either.

O.K., on with the discovery... Remember when we added fractions such as 2/5 + 1/4? We needed to find a common denominator before we could add. Also we needed to simplify the final answer. With decimals we don't need to bother with all of this. If we write the fractions in decimal form, then we can easily add them.

2/5 = .4   .4 0
1/4 = .25 + .2 5
      .6 5
         

So how do we write fractions in decimal form? E.g., how do we write 2/5 as a decimal?

Divide the denominator into the numerator.  Notice that the divisor 5 is greater than the dividend 2, so we need to write a decimal point and place some zeros to the right of it. Now we can divide 5 into 20. Make sure to copy the decimal point into the quotient so it is directly above the original.

So we get which means that 2/5 = .40 or more simply, 2/5 = .4 since trailing zeros after the decimal are usually not written. (Although zeros are used to indicate significant figures in physics, chemistry, etc. where the accuracy of measurement data needs to be indicated.) Sometimes you will see a zero written in front of the decimal point, in which case the answer would look like 2/5 = 0.4

Now let's look at another fraction. What happens when we have a fraction such as 1/3? How can we write this as a decimal?

This process continues, and we get 1/3 = .33333...
and it's apparent that this will never stop, no matter how far we carry this out. This is called a repeating decimal.

We can now see that some fractions can't be written exactly in decimal form. E.g., 1/9 = .1111111111... In answer to the above question: Why not use decimals all the time? The answer could be that in some cases, fractions can be better suited to the problem. In other words, in some cases fractions can actually be easier to work with than with decimals.

To write fractions as decimals:
  1. Divide the denominator into the numerator.
  2. Write a decimal point at the end of the dividend (if there isn't already a decimal point somewhere in the number).
  3. Place some zeros at the end of the dividend.
  4. Copy the location of the decimal point into your quotient.
  5. Divide the denominator into the numerator. (You can ignore the decimal point in this step.)
  6. You can keep putting zeros on the end of the dividend and repeating the above steps until you reach the necessary accuracy.
To write decimals as fractions:
  1. Write the whole number by itself (Any digits to the left of the decimal point would be the whole number.)
  2. Count the number of decimal places to the right of the decimal point.
  3. Write this many zeros in the denominator.
  4. Write a 1 in front of the zeros.
  5. Finally, write the numerator. This is the number which is to the right of the decimal point. (Don't write the decimal point. Any leading zeros are omitted.)

 Now try it...

  1. Write 5/8 as a decimal.
  2. Write .125 as a fraction.
  3. For a challenge, try writing directions for converting fractions to decimals. Write the directions in your own words without looking at a textbook. Next, try having someone follow your directions and see if they can correctly write fractions as decimals. (You could write your directions in the Discussion Board area.)

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