Section A: Practice Problems Decimals with Tenths and Hundredths

Section Summary

Details

In this section, we learned to express tenths and hundredths as decimals, locate them on a number line, and compare them.

We learned that $\frac{1}{10}$ written as a decimal is 0.1, and that this number is also read “1 tenth.” $\frac{1}{100}$ written as a decimal is 0.01 and is read “1 hundredth.”

The table shows some more examples of tenths and hundredths in their decimal notation.

Because $\frac{5}{10}$ and $\frac{50}{100}$ are equivalent, the decimals 0.5 and 0.50 are also equivalent.
Likewise, $\frac{17}{10}$ and $\frac{170}{100}$ are equivalent, so 1.7 and 1.70 are also equivalent.

fraction	decimal
$\frac{4}{100}$	0.04
$\frac{23}{100}$	0.23
$\frac{5}{10}$	0.5
$\frac{50}{100}$	0.50
$\frac{17}{10}$	1.7
$\frac{170}{100}$	1.70

Just like fractions, decimals can be located on a number line. Doing so can help us compare them.

For instance, 0.24 is equivalent to $\frac{24}{100}$ , which is between $\frac{20}{100}$ and $\frac{30}{100}$ (or between $\frac{2}{10}$ and $\frac{3}{10}$ ) on the number line. We can see that 0.24 is greater than 0.08 and less than 0.61.

Number line. 13 evenly spaced tick marks. First tick mark, 0. Eleventh tick mark, 1. Points with labels at 8 hundredths, 24 hundredths, 61 hundredths, 96 hundredths, 1 and 12 hundredths.

Problem 1 (Pre-Unit)

Round each number to the nearest 10 and to the nearest 100.

Problem 2 (Pre-Unit)

A number $P$ is located on the number line.

Number line. Scale 600 to 800, by 100's. Point P, over halfway between 600 and 700.

Round $P$ to the nearest multiple of 100. Explain your reasoning.
Can you tell what $P$ is if rounded to the nearest multiple of 10? Explain your reasoning.

Problem 3 (Pre-Unit)

Find the value of each expression. Show your reasoning.

$523 + 278$
$418 - 235$

Problem 4 (Pre-Unit)

Here are three numbers: 265, 652, and 526. For each question, explain your reasoning.

Does the digit 6 have a greater value in 265 or 652?
Does the digit 5 have a greater value in 265 or 652?
In which number does the digit 2 have the greatest value? In which one does it have the least value?

Problem 5 (Lesson 1)

Each large square represents 1.

Write a fraction and a decimal that represent the shaded part of the large square.
Fraction:
Decimal:
Shade a part of each square to represent each given number.
Fraction: $\frac{13}{100}$
Decimal:
Fraction:
Decimal: 0.44

Problem 6 (Lesson 2)

Select all the numbers equivalent to $\frac{2}{10}$ .

0.5
0.2
$\frac{20}{100}$
$\frac{25}{100}$
0.20

Problem 7 (Lesson 3)

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

Problem 8 (Lesson 4)

Order the numbers from least to greatest:

5.90
9.05
5.95
0.59
5.59

Problem 9 (Lesson 5)

Order the numbers from least to greatest:

$\frac{13}{10}$
1.25
1.46
$\frac{7}{5}$
$\frac{155}{100}$

Problem 10 (Exploration)

The table shows the distances, in miles, some students walked during the school week.

Order the numbers from least to greatest.

student	distance (miles)
Han	$5 \frac{3}{4}$
Tyler	$5 \frac{7}{8}$
Mai	$5.95$
Elena	$5 \frac{8}{10}$
Andre	$5.79$

Problem 11 (Exploration)

In a recent lesson, you learned about the lengths of the jumps made by Carl Lewis and other athletes.

Create and label a number line to show the distances of all ten jumps made by the athletes.