Lesson 3 Decimals on Number Lines

- Let’s compare some decimals.

Warm-up Which One Doesn’t Belong: Decimals and Fractions

Which one doesn’t belong?

eight tenths
$\frac{80}{10}$
$.80$

Activity 1 Points on Number Lines

Problem 1

Label each tick mark on the number line with the number it represents.

Number line. 13 evenly spaced tick marks. First tick mark, 0. Eleventh tick mark, 1.

Problem 2

Here are eight numbers.

0.10
0.40
0.80
1.10
0.15
0.45
0.75
1.05

Locate and label each number on the number line.
Which number is greatest? Which is least? Explain how the number line can help determine the greatest and least numbers.

Problem 3

Locate and label these numbers on the number line.

0.24
0.96
0.61
1.12
0.08

Problem 4

Use two numbers from the previous questions to complete each comparison statement so that it is true.

is greater than .
is less than .
is the greatest number.

Activity 2 Decimals Compared

Problem 1

Here is a number line with two points on it.

Number line. First tick mark, 0. Second tick mark, 1 tenth. Fifth tick mark, labeled, point A. Point B in between sixth and seventh tick mark, but closer to the seventh tick mark.

Name the decimal located at point A.
Is the decimal at point A less than or greater than 0.50? Explain or show your reasoning.
Is the decimal at point B greater or less than 0.06? Explain your reasoning.
Estimate the decimal at point B.

Problem 2

Compare the numbers using $<$ , $>$ , or $=$ . Can you think of a way to make comparisons without using a number line? Be prepared to share your thinking.

$0.51$ $0.09$
$0.19$ $0.91$
$0.45$ $0.54$
$0.62$ $0.26$
$1.02$ $0.95$
$0.3$ $0.30$
$4.01$ $4.10$

Practice Problem

Problem 1

Locate and label 0.6 and 0.35 on the number line.
Compare 0.6 and 0.35 using < or >.