Question

1. lisa writes the following list of numbers. 5.737737773..., 26, √45, -3/2, 0, 9 a. which numbers are rational? b. which numbers are irrational?

Explanation:

Part a

Step1: Recall rational number definition

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. Integers, fractions, terminating decimals, and repeating decimals are rational.

Step2: Analyze each number

• $5.737737773...$: Non - repeating, non - terminating decimal (irrational).
• $26$: Integer, can be written as $\frac{26}{1}$ (rational).
• $\sqrt{45}=3\sqrt{5}$, $\sqrt{5}$ is irrational, so $\sqrt{45}$ is irrational.
• $-\frac{3}{2}$: Fraction (rational).
• $0$: Integer, $\frac{0}{1}$ (rational).
• $9$: Integer, $\frac{9}{1}$ (rational).

Step1: Recall irrational number definition

An irrational number is a number that cannot be expressed as $\frac{p}{q}$ ( $p,q$ integers, $q
eq0$), non - repeating, non - terminating decimals and square roots of non - perfect squares are irrational.

Step2: Analyze each number

• $5.737737773...$: Non - repeating, non - terminating decimal (irrational).
• $26$: Rational (as above).
• $\sqrt{45}=3\sqrt{5}$, $\sqrt{5}$ is irrational, so $\sqrt{45}$ is irrational.
• $-\frac{3}{2}$: Rational (as above).
• $0$: Rational (as above).
• $9$: Rational (as above).

Answer:

The rational numbers are $26$, $-\frac{3}{2}$, $0$, $9$.

Part b