Decimals and Fractions on the Number Line
Now, what about decimals (numbers with a decimal point) and fractions (numbers representing a part of a whole)? How do we find and plot these numbers? For these types of numbers, first we have to realize that they tell you that your number is more than a whole number. These numbers have a part of a whole number included. For example, the decimal 3.5 tells you that you have three whole things and then half a thing. If we thought about it in terms of pies, we would have three whole pies and then half of a pie. So, the numbers after the decimal point tell you how much of another whole you have - how much of another pie you have.
Fractions are related to decimals, as you can go back and forth between fractions and most decimals. For example, the fraction 3 1/2 can be converted to our decimal 3.5. We made the conversion by dividing the 1 and the 2 and then adding it to the 3. This is the kind of conversion we would make for mixed fractions. If we had the fraction 7/2, on the other hand, we would do a straight division to find our decimal. 7 divided by 2 is also 3.5. All these numbers are the same.
The way that makes the most sense for me when looking for fractions on a number line is to convert these to decimals first and then to look for them. And this is what I want you to do. Convert your fractions to decimal before working with them on the number line.
To find your decimal or fraction turned into a decimal on the number line, we first find our whole number part and then we figure out how much more we need to go for the part after the decimal, the part of a whole. For example, to find the number 3.5, we first find our 3. We find this by going 3 spaces to the right of 0. Now we need to figure out how much we have to go to account for the .5 after the three. To do this, we can put little slash marks between our 3 and 4 to divide this section into 10 spaces.
We would end up putting down 9 equally spaced tick marks to divide this area into 10 equal spaces. Now we can count and find the fifth tick mark to find our .5. If our decimal was 3.53, we would do what we did to find 3.5, and then we would divide the next space into 10 spaces just like we did to find the .5 so we can find our .53. Make these tick marks little so you can tell that these are even smaller than the other tick marks you drew. Our .53 would then be the third little tick mark after our .5
To plot these numbers, you first find them on the number line, then you draw a point at that spot. So, to plot the number 3.5, you first find it and then you place a nice big dot at that location.
Comparing the Numbers on the Number Line
Now that you know how to find and plot numbers, let's talk about comparing these numbers. Let's say you want to compare the numbers 5 and 6.5. You would first plot both of these numbers by finding them and then putting a dot on them. Label these dots so you know which number is which.
Now your job is to see which one is bigger. Because our number line gets bigger when you go to the right, the dot that is to the right of the other dot will be bigger. So, comparing our numbers 5 and 6.5, we see that 6.5 is bigger than 5. 5, then, is smaller than 6.5. And there we have it. This is how you use a number line to compare numbers.