Placing & Finding Decimals on a Number Line

Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Decimals are what happens when you break a single piece into tenths, like changing a dollar for dimes or a dime for pennies. In this lesson, we'll explore how to find decimal numbers on the number line.

What are Decimals? What's a Number Line?

Okay, so you finally got it down. You can find numbers on the number line. You can find 5, -3, 6, 0, and so on. Now they throw a wrench in the works. They want you to find decimals like 2.3. How do you do that?

A number line is just a straight line, sort of like a ruler, but with positive numbers listed by increasing values to the right of 0 and negative numbers listed by increasingly negative values to the left. Normally, a number line will only show whole numbers (0 and positive counting numbers, like 1, 2, and 3) and negative integers (like -1, -2, and -3).

Decimals are parts of whole numbers, divided by multiples of 10. For example, .3 is three tenths of 1. It's sort of like cutting a pizza into 10 equal slices and then taking three slices. You have three tenths of the pizza. If you had two whole pizzas to go with your three slices, you would have 2.3 pizzas. Notice how the whole numbers end up on the left side of the decimal point, while the smaller pieces are on the right side.

Decimals can get a lot smaller, too. You could cut each pizza slice into 10 equal pieces (which would make hundredths), and then even cut one of those pieces into ten pieces (which would make thousandths). So if we picked up a couple of whole pizzas, three of the tenths, two of the hundredths, and four of the thousandths, we would now have 2.324 pizzas. See how each of the decimal places fits in? In the remainder of this lesson we will just focus on tenths, leaving the smaller decimal pieces for a later lesson.

Breaking Down the Number Line

Realize that decimals are always based on the number 10. The name 'decimal' comes from Medieval Latin decimalis, which means a tenth part. To show tenths on a number line you divide that space between each of the whole numbers into 10 equal parts. Each of those parts is a tenth of a whole number. Take a look at Figure 1. The number line is shown with the spaces between the numbers divided into tenths.


Figure 1. Decimals on the number line
decimal number line


If we wish, we can label those divisions to help us identify the decimal places. Figure 2 shows a little bit of what that would look like.


Figure 2. Labeled decimals on the number line
decimal number line


Notice how each of the decimal places is labeled with the whole number it's attached to, plus the added decimal value. Sometimes the 0 is left off when the number is between 1 and -1, but any other place on the number line you'll see a whole number in front of the decimal.

Finding Decimal Numbers on the Number Line

So say you want to find 2.3, as we mentioned before. To start, find the 2 on the number line. Since 2.3 is bigger than 2, you know you'll have to go to the right on the number line toward 3. Divide the space between 2 and 3 into ten equal parts. Once you've done that, count three of those parts to the right of the 2, and you've found it! Figure 3 shows where that would be.


Figure 3. Finding 2.3 on a number line
decimal number line


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