## Locating decimals on a number line

0.362 can be placed on a number line by first looking at the numbers 0.3 and 0.36

 Units . Tenths Hundredths Thousandths 0 . 3 6 2

The number 0.3 is equal to the fraction $\frac{3}{10}$, so we need to cut the interval from 0 to 1 into ten equal intervals and locate 0.3 at the third interval marker.

The number 0.36 is equal to $\frac{36}{100}$, which can be written as

$\frac{3}{10}+\frac{6}{100}$

in expanded form. Since 6 is in the hundredths place, we need to cut the interval from 0 to 1 into 100 equal intervals. But since 0 to 1 is already cut into ten intervals, we can cut each of those smaller intervals into ten even smaller intervals. The result is 100 equal intervals from 0 to 1. The number 0.36 is placed 6 small intervals beyond 0.3.

Finally, the number 0.362 is equal to $\frac{362}{1000}$, which is written in expanded form as

$\frac{3}{10}+\frac{6}{100}+\frac{2}{1000}$

Since 2 is in the thousandths place, we need to cut the interval between 0.36 and 0.37 into ten equal sized intervals. 0.362 will be placed at the second interval beyond 0.36.

Now it is easy to compare decimals. Numbers further to the right are larger than numbers to the left. For example, 0.362 is bigger than 0.36, but smaller than 0.37.

 Directions: Use the sliders to create a number. As you move the slides, notice how the locator arrow moves around. Click "Show" to add or remove numbers. Click "Compare numbers" to see how the two numbers compare with one another. What you should learn: How does the arrow move when you use the "tenths" slider compared to when you use the "thousandths" slider? Duane Habecker, Created with GeoGebra

This next applet includes negative decimals.

 Directions: Place points A, B, and C where they should go. Check the box to see how accurate you are. Click the blue arrows for another set of decimals to locate. Duane Habecker, Created with GeoGebra

# Self-Check

Question 1

Which is the best estimation for the location of Point A on the number line?
1.5?  1.9? 1.19? 0.5?

Question 2

Which is the best estimation for the location of Point A on the number line?

-1.5? 0.75? -0.5? 0.5?

Question 3

Which is the best estimation for the location of Point A on the number line?

2.63? 0.6? 3.45? 1.53?