Lesson 1: Practice 2 Solutions

Truth or Tale! Categorize each statement below as a Truth (a mathematically true statement) or Tale (an untrue statement).

	Truth	Tale	Explanation
−18 can be classified as an integer and a rational number.	X		−18 is both a rational number and an integer.
All decimals are irrational numbers.		X	Decimals that terminate or repeat are rational numbers, so not all decimals can be classified as irrational.
$\frac{- 26}{4}$ and $5.85714285340 . . .$ are both rational numbers.		X	$\frac{- 26}{4}$ can be simplified to $- 6.5$ which is a rational number. $5.85714285340 . . .$ is an irrational number.
To plot an irrational number on a number line, you have to round it first.	X		Irrational numbers have too many digits to plot them as they are. To plot irrational values on a number line, they need to be rounded to a more usable value.
163.25 can be classified as a rational number and an integer.		X	163.25 is a rational number. Decimals are not integers, so 163.25 can not be classified as an integer.
$\frac{108}{18}$ can be simplified to an integer.	X		$\frac{108}{18}$ can be simplified to a positive whole number of 6, which can be classified as an integer.
$\frac{13}{3}$ is an irrational number.		X	$\frac{13}{3}$ can be rewritten as the repeating decimal $13.33$ , which is a rational number.
0 is a whole number but not a natural number.	X		0 can be classified as a whole number. Natural numbers are positive and used for counting objects. 0 does not have a positive value and is not used in counting objects, it is not a natural number.
9.46903281… can be represented on a number line as 9.5.	X		9.46903281… is an irrational number, which can be rounded to 9.5 when plotted on a number line.
−45 is an integer and a whole number.		X	−45 is an integer. Whole numbers do not include negative values, so −45 is not a whole number.

Construct a number line and plot the terms:

$\frac{56}{10}, 5.2, 5.7630142791 . . .$

Construct a number line and plot the terms:

$25 \frac{2}{3}, 25.010437218, 25.33$

25.010437218… can be rounded to 25.

Which of the following terms is represented by the X on the number line?

$\frac{- 71}{5}, - 14.780354690321 . . ., \frac{- 72}{5}$

The x on the number line represents the value −14.780354690321…, which can be rounded to and plotted as 14.8.

Myra wants to plot the following value on a number line, but she can’t decide on a range to use for her number line. Determine a range that will work for Myra’s number line, and give reasons to support your choice.

$\frac{17}{5}$

This fraction can be simplified to the decimal 3.4.
3.4 is between 3 and 4, so the range of the number line should be 3 to 4.

Gregory and Jin are having a discussion about the value −75. Gregory wants to classify −75 as a rational number, a whole number, and an integer. Jin wants to classify the number as a rational number and an integer. Who is correct? Give reasons to support your choice.

Jin is correct. The number −75 can be classified as a rational number and an integer. George is incorrect because the number −75 can not be classified as a whole number. The category “whole numbers” includes positive whole numbers greater than 0, but does not include negative numbers.