ahron j vav date ______ lg: i can classify real numbers into the correct subsets
level 2
identify the sets to which each of the following numbers belongs by marking an \x\ in the appropriate box(es).

| | rational | irrational |
|-------|----------|------------|
| 1) | π | |
| 2) | 2.878787 ... | |
| 3) | √36 | |
| 4) | √23 | |
| 5) | 5/3 | |
| 6) | 8.25371 ... | |

7) circle the expression that is rational.
a. 6½ − π b. 2.555 ... + √12 c. 2√2 · 3√6 d. √16 − 4⅓
8) which terms can be used to classify the expression −7.
a. integer, rational, and real b. irrational and real
c. whole and irrational d. rational and real

place an x in the table to show how many significant digits are in each number.

| number | number of significant digits |
|----------|------------------------------|
| | two | three | four |
| 1.02 | | | |
| 0.0034 | | | |
| 321,000 | | | |
| 0.4596 | | | |

write in rational exponent form
13) ∛x⁸
14) ⁵√g³
write in radical form
15) a^(7/9)
16) w^(2/5)

Question

ahron j vav date ______ lg: i can classify real numbers into the correct subsets
level 2
identify the sets to which each of the following numbers belongs by marking an \x\ in the appropriate box(es).

|       | rational | irrational |
|-------|----------|------------|
| 1)    | π        |            |
| 2)    | 2.878787 ... |          |
| 3)    | √36      |            |
| 4)    | √23      |            |
| 5)    | 5/3      |            |
| 6)    | 8.25371 ... |          |

7) circle the expression that is rational.
   a. 6½ − π    b. 2.555 ... + √12    c. 2√2 · 3√6    d. √16 − 4⅓
8) which terms can be used to classify the expression −7.
   a. integer, rational, and real    b. irrational and real
   c. whole and irrational          d. rational and real

place an x in the table to show how many significant digits are in each number.

| number   | number of significant digits |
|----------|------------------------------|
|          | two | three | four |
| 1.02     |     |       |      |
| 0.0034   |     |       |      |
| 321,000  |     |       |      |
| 0.4596   |     |       |      |

write in rational exponent form
13) ∛x⁸
14) ⁵√g³
write in radical form
15) a^(7/9)
16) w^(2/5)

Accepted Answer

### Problem 1: Classify $\pi$
# Explanation:
## Step1: Recall rational/irrational def
A rational number can be expressed as $\frac{p}{q}$ ($p,q$ integers, $q
eq0$), irrational cannot. $\pi$ is non - repeating, non - terminating, so irrational.
# Answer:
Irrational: X (Rational: no X)

### Problem 2: Classify $2.878787\cdots$
# Explanation:
## Step1: Identify number type
$2.878787\cdots$ is a repeating decimal. Repeating decimals can be written as a fraction (e.g., let $x = 2.8787\cdots$, $100x=287.8787\cdots$, $99x = 285$, $x=\frac{285}{99}$), so it's rational.
# Answer:
Rational: X (Irrational: no X)

### Problem 3: Classify $\sqrt{36}$
# Explanation:
## Step1: Simplify the square root
$\sqrt{36}=6$, and $6=\frac{6}{1}$, which is a rational number (integer, hence rational).
# Answer:
Rational: X (Irrational: no X)

### Problem 4: Classify $\sqrt{23}$
# Explanation:
## Step1: Analyze the square root
23 is not a perfect square, so $\sqrt{23}$ is a non - repeating, non - terminating decimal. Thus, it's irrational.
# Answer:
Irrational: X (Rational: no X)

### Problem 5: Classify $\frac{5}{3}$
# Explanation:
## Step1: Recall rational definition
$\frac{5}{3}$ is in the form $\frac{p}{q}$ ($p = 5$, $q = 3$, integers, $q
eq0$), so it's rational.
# Answer:
Rational: X (Irrational: no X)

### Problem 6: Classify $8.25371\cdots$
# Explanation:
## Step1: Check decimal type
$8.25371\cdots$ is a non - repeating, non - terminating decimal, so it's irrational.
# Answer:
Irrational: X (Rational: no X)

### Problem 7: Circle the rational expression
# Explanation:
## Step1: Analyze option a
$6\frac{1}{2}-\pi$: $\pi$ is irrational, so the result is irrational.
## Step2: Analyze option b
$2.555\cdots+\sqrt{12}$: $\sqrt{12}=2\sqrt{3}$ (irrational), so the result is irrational.
## Step3: Analyze option c
$2\sqrt{2}\cdot3\sqrt{6}=6\sqrt{12}=6	imes2\sqrt{3}=12\sqrt{3}$ (irrational).
## Step4: Analyze option d
$\sqrt{16}-4\frac{1}{3}=4 - \frac{13}{3}=\frac{12 - 13}{3}=-\frac{1}{3}$, which is rational.
# Answer:
d. $\sqrt{16}-4\frac{1}{3}$

### Problem 8: Classify $-7$
# Explanation:
## Step1: Recall number sets
-7 is an integer (integers are rational as $-7=\frac{-7}{1}$), and all integers are real numbers. So it's integer, rational, and real.
# Answer:
a. integer, rational, and real

### Problem: Significant Digits
#### For 1.02:
# Explanation:
## Step1: Count significant digits
Significant digits: 1, 0, 2? Wait, no: non - zero digits and zeros between non - zeros are significant. 1.02 has three significant digits (1, 0, 2).
# Answer:
Three: X

#### For 0.0034:
# Explanation:
## Step1: Count significant digits
Leading zeros are not significant. So 3 and 4 are significant, two significant digits.
# Answer:
Two: X

#### For 321,000:
# Explanation:
## Step1: Count significant digits
Trailing zeros in a whole number without a decimal are ambiguous, but assuming it's 321000 (the non - zero digits are 3, 2, 1), three significant digits.
# Answer:
Three: X

#### For 0.4596:
# Explanation:
## Step1: Count significant digits
All non - zero digits and zeros? Wait, 0.4596: 4, 5, 9, 6 are significant, four significant digits.
# Answer:
Four: X

### Problem 13: Write $\sqrt[3]{x^{8}}$ in rational exponent form
# Explanation:
## Step1: Recall radical - exponent rule
$\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$. Here, $n = 3$, $m = 8$, so $\sqrt[3]{x^{8}}=x^{\frac{8}{3}}$.
# Answer:
$x^{\frac{8}{3}}$

### Problem 14: Write $\sqrt[5]{g^{3}}$ in rational exponent form
# Explanation:
## Step1: Apply radical - exponent rule
Using $\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$, with $n = 5$, $m = 3$, we get $\sqrt[5]{g^{3}}=g^{\frac{3}{5}}$.
# Answer:
$g^{\frac{3}{5}}$

### Problem 15: Write $a^{\frac{7}{9}}$ in radical form
# Explanation:
## Step1: Recall exponent - radical rule
$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. Here, $n = 9$, $m = 7$, so $a^{\frac{7}{9}}=\sqrt[9]{a^{7}}$.
# Answer:
$\sqrt[9]{a^{7}}$

### Problem 16: Write $w^{\frac{2}{5}}$ in radical form
# Explanation:
## Step1: Apply exponent - radical rule
Using $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, with $n = 5$, $m = 2$, we get $w^{\frac{2}{5}}=\sqrt[5]{w^{2}}$.
# Answer:
$\sqrt[5]{w^{2}}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Classify $\pi$

Step1: Recall rational/irrational def

Step1: Identify number type

Step1: Simplify the square root

Answer:

Problem 2: Classify $2.878787\cdots$