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. It ends at the 4.
Fraction to Decimal
Now that we know how to turn a decimal into a fraction, let's now see how easy it is to turn a fraction into a decimal. There is only one step involved in this process and that is to divide. The easy way I use to remember this step is to just look at the slash symbol. What does that tell me to do? It tells me to divide. So, I will.
For the fraction 1/4, to turn that into a decimal, I will simply divide 1 by 4. I can either use a calculator or do it by hand using long division. My answer is 0.25. The fraction 1/4 is 0.25 as a decimal.
Lesson Summary
In review:
- Decimals are numbers with a decimal point, and fractions are two whole numbers with a slash in between them.
- To convert from a decimal to a fraction, we view the decimal number in two parts, the part before the decimal point as a whole number and the part after the decimal point as a part of a whole. We then turn the part of the whole into a fraction by dividing by the last place value of the decimal and simplify. Then, we add this part to the whole part to get our answer in standard form.
- One important thing to remember is that we can't convert a never-ending decimal whose digits never repeat into a fraction.
- To convert a fraction into a decimal, simply look at the slash and do as it tells you to do. Divide the two numbers to get your decimal. Use either a calculator or do it by hand using long division.
Learning Outcomes
After you've completed this lesson, you'll have the ability to:
- Convert fractions into decimals and decimals into fractions
- Explain what to do with decimals that never end and whose numbers don't repeat