classifying numbers
directions: identify whether each number is rational or irrational and circle the correct choice.
1) -345 = rational or irrational
2) 890023 = rational or irrational
3) $\frac{2}{5}$ = rational or irrational
4) 3.271 = rational or irrational
5) $6.\overline{7}$ = rational or irrational
6) $\sqrt{28}$ = rational or irrational
7) -2.5 = rational or irrational
8) $\frac{30}{1}$ = rational or irrational
9) $\sqrt{16}$ = rational or irrational
10) $-4\frac{9}{17}$ = rational or irrational
11) 17.252252225... = rational or irrational
12) $\pi$ = rational or irrational
13) 0 = rational or irrational
14) $0.\overline{3}$ = rational or irrational
15) $\sqrt{0.04}$ = rational or irrational
16) -7 = rational or irrational
17) 42 = rational or irrational
18) $3^5$ = rational or irrational
19) $\frac{13}{4}$ = rational or irrational
20) $(-6)^3$ = rational or irrational
21) 5.24956348... = rational or irrational
22) $\frac{0}{12}$ = rational or irrational

Question

Accepted Answer

### 1) -345
# Explanation:
## 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 are rational.
## Step2: -345 is an integer.
Integers can be written as $\frac{-345}{1}$, so it's rational.
# Answer: Rational

### 2) 890023
# Explanation:
## Step1: Recall rational number definition.
Integers are rational as they can be written as $\frac{n}{1}$ ($n$ integer, $1
eq0$).
## Step2: 890023 is an integer.
So it can be expressed as $\frac{890023}{1}$, hence rational.
# Answer: Rational

### 3) $\frac{2}{5}$
# Explanation:
## Step1: Recall rational number definition.
A number in the form $\frac{p}{q}$ ($p,q$ integers, $q
eq0$) is rational.
## Step2: $\frac{2}{5}$ fits the form.
Here $p = 2$, $q = 5$ (integers, $5
eq0$), so it's rational.
# Answer: Rational

### 4) 3.271
# Explanation:
## Step1: Recall rational number definition.
Terminating decimals are rational as they can be written as a fraction.
## Step2: Convert 3.271 to fraction.
$3.271=\frac{3271}{1000}$, where 3271 and 1000 are integers, $1000
eq0$. So rational.
# Answer: Rational

### 5) $6.\overline{7}$
# Explanation:
## Step1: Recall rational number definition.
Repeating decimals are rational as they can be expressed as a fraction.
## Step2: Let $x = 6.\overline{7}$, then $10x=67.\overline{7}$, subtract: $10x - x=67.\overline{7}-6.\overline{7}\Rightarrow9x = 61\Rightarrow x=\frac{61}{9}$. So rational.
# Answer: Rational

### 6) $\sqrt{28}$
# Explanation:
## Step1: Simplify $\sqrt{28}$.
$\sqrt{28}=\sqrt{4	imes7}=2\sqrt{7}$.
## Step2: Recall irrational number definition.
$\sqrt{7}$ is irrational (not a perfect square root), and multiplying by a non - zero rational number (2) keeps it irrational. So $\sqrt{28}$ is irrational.
# Answer: Irrational

### 7) -2.5
# Explanation:
## Step1: Recall rational number definition.
Terminating decimals are rational.
## Step2: Convert -2.5 to fraction.
$-2.5=-\frac{25}{10}=-\frac{5}{2}$, which is $\frac{p}{q}$ form ($p=-5,q = 2$, integers, $q
eq0$). So rational.
# Answer: Rational

### 8) $\frac{30}{1}$
# Explanation:
## Step1: Recall rational number definition.
A number in $\frac{p}{q}$ form ($p,q$ integers, $q
eq0$) is rational.
## Step2: $\frac{30}{1}$ fits the form.
Here $p = 30$, $q = 1$ (integers, $1
eq0$), so rational.
# Answer: Rational

### 9) $\sqrt{16}$
# Explanation:
## Step1: Simplify $\sqrt{16}$.
$\sqrt{16}=4$.
## Step2: Recall rational number definition.
4 is an integer, so it can be written as $\frac{4}{1}$, hence rational.
# Answer: Rational

### 10) $-4\frac{9}{17}$
# Explanation:
## Step1: Convert mixed number to improper fraction.
$-4\frac{9}{17}=-\frac{4	imes17 + 9}{17}=-\frac{68 + 9}{17}=-\frac{77}{17}$.
## Step2: Recall rational number definition.
It is in $\frac{p}{q}$ form ($p=-77,q = 17$, integers, $q
eq0$), so rational.
# Answer: Rational

### 11) 17.252252225...
# Explanation:
## Step1: Recall irrational number definition.
A non - repeating, non - terminating decimal is irrational.
## Step2: Analyze 17.252252225...
The decimal does not repeat in a fixed pattern and is non - terminating, so it's irrational.
# Answer: Irrational

### 12) $\pi$
# Explanation:
## Step1: Recall $\pi$'s properties.
$\pi$ is a non - repeating, non - terminating decimal ($\pi\approx3.1415926535\cdots$).
## Step2: Recall irrational number definition.
Non - repeating, non - terminating decimals are irrational, so $\pi$ is irrational.
# Answer: Irrational

### 13) 0
# Explanation:
## Step1: Recall rational number definition.
0 can be written as $\frac{0}{1}$, where $p = 0$, $q = 1$ (integers, $q
eq0$).
## Step2: So 0 is rational.
# Answer: Rational

### 14) $0.\overline{3}$
# Explanation:
## Step1: Recall rational number definition.
Repeating decimals are rational. Let $x = 0.\overline{3}$, then $10x=3.\overline{3}$, subtract: $10x - x=3.\overline{3}-0.\overline{3}\Rightarrow9x = 3\Rightarrow x=\frac{1}{3}$.
## Step2: So it's in $\frac{p}{q}$ form, hence rational.
# Answer: Rational

### 15) $\sqrt{0.04}$
# Explanation:
## Step1: Simplify $\sqrt{0.04}$.
$\sqrt{0.04}=0.2$.
## Step2: Recall rational number definition.
0.2 is a terminating decimal, and can be written as $\frac{2}{10}=\frac{1}{5}$, so rational.
# Answer: Rational

### 16) -7
# Explanation:
## Step1: Recall rational number definition.
Integers are rational as they can be written as $\frac{n}{1}$ ($n$ integer, $1
eq0$).
## Step2: -7 is an integer, so $\frac{-7}{1}$, hence rational.
# Answer: Rational

### 17) 42
# Explanation:
## Step1: Recall rational number definition.
Integers are rational as they can be written as $\frac{n}{1}$ ($n$ integer, $1
eq0$).
## Step2: 42 is an integer, so $\frac{42}{1}$, hence rational.
# Answer: Rational

### 18) $3^{5}$
# Explanation:
## Step1: Calculate $3^{5}$.
$3^{5}=3	imes3	imes3	imes3	imes3 = 243$.
## Step2: Recall rational number definition.
243 is an integer, so $\frac{243}{1}$, hence rational.
# Answer: Rational

### 19) $\frac{13}{4}$
# Explanation:
## Step1: Recall rational number definition.
A number in $\frac{p}{q}$ form ($p,q$ integers, $q
eq0$) is rational.
## Step2: $\frac{13}{4}$ fits the form.
Here $p = 13$, $q = 4$ (integers, $4
eq0$), so rational.
# Answer: Rational

### 20) $(-6)^{3}$
# Explanation:
## Step1: Calculate $(-6)^{3}$.
$(-6)^{3}=(-6)	imes(-6)	imes(-6)=-216$.
## Step2: Recall rational number definition.
-216 is an integer, so $\frac{-216}{1}$, hence rational.
# Answer: Rational

### 21) 5.24956348...
# Explanation:
## Step1: Recall irrational number definition.
A non - repeating, non - terminating decimal is irrational.
## Step2: Analyze 5.24956348...
The decimal does not repeat in a fixed pattern and is non - terminating, so it's irrational.
# Answer: Irrational

### 22) $\frac{0}{12}$
# Explanation:
## Step1: Recall rational number definition.
A number in $\frac{p}{q}$ form ($p,q$ integers, $q
eq0$) is rational.
## Step2: $\frac{0}{12}$ fits the form.
Here $p = 0$, $q = 12$ (integers, $12
eq0$), and $\frac{0}{12}=0$, so rational.
# Answer: Rational

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QUESTION IMAGE

Question

Explanation:

1) -345

Step1: Recall rational number definition.

Step2: -345 is an integer.

Step1: Recall rational number definition.

Step2: 890023 is an integer.

Step1: Recall rational number definition.

Step2: $\frac{2}{5}$ fits the form.

Answer:

2) 890023