7.1 Rational and Irrational Numbers

Before you get started, take this readiness quiz.

Write $3.19$ as an improper fraction.
If you missed this problem, review the reference.

Write $\frac{5}{11}$ as a decimal.
If you missed this problem, review the reference.

Simplify: $\sqrt{144} .$
If you missed this problem, review the reference.

Write each as the ratio of two integers: ⓐ $−15$ⓑ $6.81$ⓒ $−3 \frac{6}{7} .$

Write each as the ratio of two integers: ⓐ $−24$ⓑ $3.57 .$

Write each as the ratio of two integers: ⓐ $−19$ ⓑ $8.41 .$

Identify each of the following as rational or irrational:

1. ⓐ $0.58 \overset{–}{3}$
2. ⓑ $0.475$
3. ⓒ $\text{3}.\text{605551275}\ldots$

Identify each of the following as rational or irrational:

ⓐ $0.29$ⓑ $0.81 \overset{–}{6}$ⓒ $\text{2}.\text{515115111}\ldots$

Identify each of the following as rational or irrational:

ⓐ $0.2 \overset{–}{3}$ⓑ $0.125$ⓒ $\text{0}.\text{418302}\ldots$

Identify each of the following as rational or irrational:

1. ⓐ $\sqrt{36}$

2. ⓑ $\sqrt{44}$

Identify each of the following as rational or irrational:

1. ⓐ $\sqrt{81}$
2. ⓑ $\sqrt{17}$

Identify each of the following as rational or irrational:

1. ⓐ $\sqrt{116}$

2. ⓑ $\sqrt{121}$

Determine whether each of the numbers in the following list is a ⓐ whole number, ⓑ integer, ⓒ rational number, ⓓ irrational number, and ⓔ real number.

Write as the ratio of two integers.

1. ⓐ $5$
2. ⓑ $3.19$

Write as the ratio of two integers.

1. ⓐ $−12$
2. ⓑ $9.279$

Determine which of the given numbers are rational and which are irrational.

$0.75$, $0.22 \overset{–}{3}$, $\text{1}.\text{39174}\ldots$

Determine which of the given numbers are rational and which are irrational.

$0 . \overset{—}{45}$, $\text{1}.\text{919293}\ldots$, $3.59$

Identify whether each number is rational or irrational.

1. ⓐ $\sqrt{25}$
2. ⓑ $\sqrt{30}$

Identify whether each number is rational or irrational.

1. ⓐ $\sqrt{164}$
2. ⓑ $\sqrt{169}$

Child care Serena wants to open a licensed child care center. Her state requires that there be no more than $12$ children for each teacher. She would like her child care center to serve $40$ children.

1. ⓐ How many teachers will be needed?

2. ⓑ Why must the answer be a whole number?

3. ⓒ Why shouldn't you round the answer the usual way?

Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.