Weight Loss Made a Bit Easier: Realistic and Practical Advice for Healthy Eating and Exercise
Available on Amazon.com in paperback/Kindle formats for $6.25/$2.99. Please click here for details.
Home | My Math and Education Books | Math Lessons | Ask a Math Question
Site Info | Contact Info | Tutoring Info | LarryZafran.com | Tweet
Lesson 90: Converting Between Decimals, Fractions, and Percents
Many students have a hard time accepting the fact that decimals, fractions, and percents are really all the same thing. In this lesson we'll explore the subject.
This lesson actually reviews a lot of the things that we've learned in previous lessons, and combines them in one place. Let's say you cut a pizza into 10 equal slices, and you eat 3 of them. You've eaten 3/10 (three tenths) of the pizza. This is easy to convert into a decimal. We know where the tenths place is, so we can just write 0.3.
To convert to a percentage involves an extra step. We know that percent means "out of 100". We need to convert our fraction to one with a denominator of 100. All we have to do is multiply numerator and denominator by 10. We then have 30/100, which is 30%.
Let's say we had some numbers that didn't work out as nicely. For example, what is 2/5 as a decimal? A fraction line is really just a dividing line. All we have to do is numerator divided by denominator, that will be our answer. We'll do 2 ÷ 5, and we get 0.4.
Here is an easy way to convert a decimal to a percentage, no matter what the decimal is. Just multiply it by 100, and add the % sign. Remember, an easy way to multiply by 100 is to just move the decimal point two spaces to the right, adding zeroes as needed. I'll start by rewriting 0.4 as 0.40. This is allowed. Moving the decimal two spaces to the right gives us 40, and we'll add the % sign, giving us 40%.
Let's say we have a percent, and we want to convert back to a decimal. We just do the opposite. We drop the % sign, and move the decimal two places to the left. For example, what is 49% as a decimal? First, we must realize that our decimal point is really to the right of the 49, even though we don't bother to write it. 49% is really 49.0% We move the decimal point two places to the left, and drop the % sign, and we get 0.490. There is no need to maintain the rightmost 0, so we just write 0.49. Notice that 0.49 is read as "forty-nine hundredths," and 49%, by definition of percent, is also forty-nine hundredths.
Memorize these procedures: To convert a/b into a decimal, compute a ÷ b. To convert a decimal to a percent, move the decimal two places to the right, and add the % sign. To convert a percent to a decimal, drop the % sign, and move the decimal point two places to the left. Practice these procedures until you are very comfortable with them.
Let's look at the three most common questions involving percents. An example of the first is: What percent of 17 is 3? An equivalent question is: 3 is what percent of 17? Here is what we do. We set up a ratio of 3 to 17, which is just a fraction: 3/17. Remember that the fraction bar is really a division sign. We just do 3 ÷ 17 to get 0.176 (rounded). Remember that to convert to a percent, which is what was asked, we move the decimal two spaces to the right, and then add the % sign. Our answer is 17.6%.
These problems are tricky, and sometimes one word in a different place can change the entire problem. Always read the problem carefully. If I'm ever getting confused about what the procedure is, what I like to do is make a simpler problem, and figure that out. For example, if I forgot what to do above, I would ask myself, "What percent of 2 is 1?", or "1 is what percent of 2?" I know that it's 50%, so that would help me remember my rule to do 1 divided by 2, and then convert to a percent.
Here is another typical percent problem. What is 18% of 57? Notice how this is a different question than the one above. Now are we given the percent that is involved, and we need to actually determine a percentage of a stated number. This is different than examining the ratio of two stated numbers, like we did above. The problem above is easy. When we see the word "of," it usually means to multiply. First we must convert 18% to a decimal. Recall that we move the decimal point two spaces to the left, to get 0.18. Now we just do 0.18 · 57 to get 10.26.
The final typical percent problem looks like: 17 is 32% of what? Notice how this question is different from the one above, even though it looks very similar. In the one above, we're taking a percentage of a number. For example, we might take 25% off the price of an item. In this example, what we are instead doing is starting with a number, but then determining a higher number, that the given number is a certain percentage of. Let's solve it, and it will make more sense.
What I will do is translate the question, step by step into symbols. First I have 17, so I'll just write that. Is means equals, so I'll write an = sign. We have 32%, and I'll write that as a decimal as 0.32. Of usually means to multiply, so I'll write my times symbol. The word "what" implies an unknown, so I'll write x. We have 17 = 0.32 · x. It seems tricky, but all I did was translate the problem one step at a time. Now we need to use basic algebra. Just divide each side by 0.32 to get x by itself. We get x = 53.1 (rounded). We found that 17 is 32% of 53.1.
These problems are quite tricky. Keep practicing them until they are not.
Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.