Decimals and Fractions
Decimals and fractions don't have to be a part of your worst math nightmare. Being able to switch between the two will actually help you solve problems faster. Let's begin our little trip into the world of decimals and fractions by briefly going over what decimals and fractions are.
If we see something like 5.4 or even 1.12, I can immediately tell you that those are decimals because decimals are the numbers that have a decimal point in them. Do you see the dot or point in both those decimal numbers?
If, on the other hand, I see something like 1/2 or 51/100, I can tell you that those are fractions because fractions are the division of two whole numbers. Fractions always have that slash between two regular numbers.
Usefulness
So, why is being able to change from one to the other useful?
The biggest reason is when you are solving math problems. If a particular math problem wants the answer in decimal form, then it will be easier to work out the problem using decimals. If, on the other hand, the math problem wants the answer in fraction form, then working the problem out using fractions will be easier.
Another reason is that sometimes an answer is easier to understand if it is in one form over the other. For example, if a teacher told you that you got 0.97 answers right on the test, would that mean much to you? Or, would it mean more if the teacher told you that you got 97/100 answers right on the test?
Decimal to Fraction
We've seen how useful being able to convert between the two is. Now let's talk about how to actually do it.
The process of changing a decimal into a fraction is a two-step process. The first step is to convert the decimal part into a fraction. The second step is to simplify that fraction and add it to the part before the decimal point. A good way to remember these two steps is to view the decimal number in two parts. View the part before the decimal point as a whole number telling you how many pies you have. Then, view the part after the decimal point as telling you how much of a whole pie you have.
So, a decimal number essentially gives you the number of whole pies plus a portion of another pie. To change this into a fraction, you would turn the partial pie into a fraction and add it to the number of whole pies to get your total pies.
Let's see how this works with a real decimal number. Let's turn the decimal 1.25 into a fraction. We are going to picture our decimal in two parts: the part before the decimal point and the part after the decimal point.
We have 1 before and 0.25 after. So, if we change these into pies, we have 1 whole pie and 0.25 of another pie. How do we turn the 0.25 into a fraction now? What we need to do now is to use our knowledge of place values to help us out. We know that the place values after the decimal point start at tenths, then goes to hundredths, then thousandths, and so on.
For our 0.25, the 2 is in the tenths place and the 5 is in the hundredths place. Because the decimal ends at the hundredths place value, we're going to use this information to turn our decimal into a fraction. Hundredths means divided by a 100, so we will divide our decimal by a 100 without the decimal point. So, we will do 25 / 100. Look at that! Doesn't that look like a fraction? Yes, it does.
Our next step is to simplify this fraction. Does 25 divide evenly into 100? Yes, it does. How many times? 25 goes into 100 four times, so we can simplify our fraction to 1/4. Because 25 divides evenly into 100, we can divide both the top and the bottom by 25. 25 divided by 25 is 1 and 100 divided by 25 is 4.
We then add our simplified fraction to our whole number to get 1 + 1/4. At this point, we can stop if the problem wants the fraction in mixed form and write 1 1/4 as our answer. Otherwise, if the problem wants the answer in standard form, we will have to add the two together. We will need to find common denominators and then add the fractions together. Our common denominator in this case is 4. Changing the 1 so that we have a denominator of 4 gives us 4/4. 4/4 + 1/4 gives us 5/4 as our standard form answer. Now we are done.
There are a couple things I want to draw your attention to. The first is the part where we turn the decimal into a fraction by dividing by the place value. We always divide by the place value of the last digit in the decimal. So, if the last digit is in the tenths place value, then we divide by 10, and if the last digit is in the thousandths place value, then we divide by 1,000.
The second thing is that if we have a decimal that never ends and whose numbers never repeat, then we can't turn it into a fraction. We can only turn decimals that end or decimals with a repeating pattern into fractions. A number like pi cannot be turned into a fraction because it has no ending. It keeps going and going and going. The approximation of pi, 3.14, can be turned into a fraction because it has an ending.