Watch this video lesson to learn how to use both fractions and decimals to help you solve problems. Learn how to change between the two to use the best one for your problem.
Fractions and Decimals
Did you know that in math, fractions and most decimals are related to each other? Yes, indeed they are. In this video lesson, you will learn about this relationship and how you can use it to your advantage in helping you to solve your problems. You will learn how to choose between the two to make your problem-solving life that much easier. So, are you ready to get going? Let's go!
We begin with a brief definition of a fraction and a decimal. A fraction is a part of a whole. It is written with a number on top, the numerator, and a number on bottom, the denominator, with either a slanted slash or a horizontal slash between the two numbers. You can think of fractions in terms of pies. The fraction 3/4, for example, means that if you cut a piece of pie into 4 slices, then 3 of those slices are yours.
A decimal is a number with a decimal point. If you go shopping at all, you will see decimal numbers everywhere. How much does lipstick cost? $7.99. That's a decimal. How much do your favorite running shoes cost? $89.99. That's a decimal.
Earlier I said that most decimals are related to fractions. The only decimals that are not related to fractions are the ones that keep on going and going and going - the ones that never end. For example, the number pi (not the pie you eat, but the mathematical constant) is not related to a fraction because it keeps going and going and never ends. Decimals and fractions are related to each other in that you can easily convert one to the other. So, let's see how this is done.
Changing to a Fraction from a Decimal
First, let's see how to go from a decimal to a fraction. It's actually quite simple. Let's try converting 7.89.
We first write the number before the decimal point down. Now we convert the number after the decimal point into a fraction. The number after the decimal point will be our top number, our numerator. Our denominator, our bottom number, will be a 1 followed by zeroes. The number of zeroes will equal the number of decimal spaces we have.
So, we count the number of digits we have after the decimal point. We count 2, so we will have 2 zeroes on the bottom following our 1. So, our decimal 7.89 turned into a fraction is 7 89/100. This is a mixed fraction.
We can turn it into an improper fraction by multiplying our whole number with the denominator and adding the numerator part of our fraction part. This will become our new numerator. So, the new numerator of 7 89/100 is 7 * 100 + 89 = 789. So, 7 89/100 turned into an improper fraction is 789/100.
See if you can turn 0.3 into a fraction. How many decimal spaces do we have? We have 1. So, how many zeroes will we have after the 1 in our denominator? We will have 1 zero. So, our fraction is 3/10.
We left our fractions as they are in both of these cases because they are already as reduced as they can be. If, however, we ended up with a fraction such as 8/10, we could reduce it to 4/5.
Changing to a Decimal from a Fraction
Now let's see how we change fractions into decimals. Let's try changing 1/8 into a decimal. Notice that the slash is the same slash that we use to mean division in algebra. Remember that part and you will know how to turn a fraction into a decimal.
Yes, you guessed it! We will divide to find our decimal. Dividing 1 by 8, we get 0.125, and there we have our decimal.
Why don't you try turning 3/4 into a decimal? What do you do? Yes, you divide 3 by 4. What do you get? 0.75. You got it!
Choosing Between Decimals and Fractions
Now, how do you decide which one to use for your problems? How do you know when to use fractions and when to use decimals?
The way you decide this is to look at your problem and see if one or the other will simplify your problem further. For example, the problem (0.5) * 2 is much easier to solve once you convert your decimal 0.5 into a fraction. Why is this?
Well, let's see what happens when we convert the 0.5 into a fraction. Converting 0.5 into a fraction, we first get 5/10. Reducing this fraction, we get 1/2. Now, (1/2) * 2 simplifies into 1 because we can cancel the 2s because we have one 2 on top and another 2 on the bottom. This means that our answer is 1, and we didn't even have to actually do math!
On the other hand, if our problem is asking us to divide 7.34 by 4, we would leave this decimal alone and go ahead with the division. Why?
If we turned it into a fraction, it wouldn't help us much because it doesn't make our problem any easier or simpler. We wouldn't be able to cancel the 4 with anything, so turning this decimal into a fraction won't help us. So, we just go ahead with our division. 7.34 divided by 4 gives us 1.835.
The key in determining whether to use a decimal or a fraction is if one or the other form will help us simplify our problem further. If it doesn't, then we leave it alone and continue with our problem.
Now, what have we learned? We've learned that a fraction is a part of a whole, and a decimal is a number with a decimal point.
Converting from a decimal to a fraction involves counting the number of decimal spaces we have. We write the whole number down first and then convert the number after the decimal point into a fraction by writing that number as the numerator, and the denominator is a 1 followed by a number of zeroes determined by the number of decimal spaces we have. To change from a fraction into a decimal, we divide the numerator by the denominator.
In determining which form to use in our problem, we choose the form that will help simplify our problem. If neither form will help simplify the problem, we leave it alone and continue solving using whatever form we are presented with.
The following objectives can be completed by watching this lesson:
- Recognize fractions and decimals
- Explain how to convert from a fraction to a decimal and from a decimal to a fraction
- Identify a tip for deciding whether to use a fraction or a decimal to solve a problem