Decimals
14 Convert Decimals to Fractions
Chad has decided he wants to work with money in fraction form and not in decimal form. Why, you ask? I don’t know. Work with me here, though, because it’s been hard to get Chad into the decimal story. Maybe he just wants his students to know a little more math. No harm there. What we’re looking at here is the following:
[latex]\LARGE0.5\text{ to }\dfrac{1}{2}[/latex]
It’s important to know how to do this in order to work with different number forms in the workplace. For instance, David, a student in Chad’s class, is a machinist. Machinists produce metal parts with a precision of up to one one-thousandth of a inch. If you are continuously working in decimals, you might forget how to work with fractions, so David wants to know how to change those decimals into fractions. The best way to illustrate how to do this is simply with an example.
Example
We’ll start with an easy decimal like 0.25 and work towards changing this into a fraction.
Step 1: Put the question into fraction form such that the decimal is over 1.
[latex]\LARGE\dfrac{0.25}{1}[/latex]
Step 2: Take both the numerator and the denominator and multiply each by 10 for every digit to the right of the decimal point. In this case, we have 2 digits to the right. Therefore, we multiply each by 100 (10 × 10).
Step 3: Reduce the fraction to its lowest terms, and we end up with the final answer.
Example
Change the decimal 0.729 into a fraction.
Step 1: Put the equation into fraction form such that the decimal is over 1.
[latex]\LARGE\dfrac{0.729}{1}[/latex]
Step 2: Take both the numerator and the denominator and multiply each by 10 for every digit to the right of the decimal point. In this case, we have 3 digits to the right. Therefore, we multiply each by 1000 (10 × 10 × 10).
Step 3: Reduce the fraction to get our final answer.
This is a tough one to reduce. My suggestion would be to do this in steps. Start with small numbers like 2 and 3. Does the number 2 go into both the numerator and the denominator? The answer would be no. How about 3? Also no. Continue this process until you find a number that works.
It is possible that you will not find a number and we are already in lowest terms. This is the case here. Our final answer is simply:
[latex]\LARGE\dfrac{729}{1000}[/latex]
Practice Questions
Try a couple practice questions and check the video answers.
Change the following decimals into fractions. Put your answer in lowest terms.
Question 1
[latex]\LARGE0.362[/latex]
Question 2
[latex]\LARGE0.963[/latex]
Now it’s time to move to a situation we might find on a job site. What was the measurement? Maybe it was something like 8 ⅜ inches. Maybe it was 2 feet, 2 ¼ inches. Those are pretty standard.
For David, the machinist, this might be exactly the type of measurement that he would get while creating metal products. But what would you do in some of the other trades?
This is the reason we need to be able to change decimals into fractions. The whole number in