Questions: π = (circumference) / (diameter) The first digits of π are 3.141592653589793238, but the digits go on forever. For every circle Circumference ÷ Diameter = π The square root of a number that isn't a perfect square is also irrational. For example, √36 is a rational number, because 36 is the square of 6. But √37 is irrational, because 37 is not the square of an integer. Check Your Understanding- Question 1 of 2 Identify each number as rational or irrational. Number Type 4 1/3 Select 8 Select √13 Select √9 Select π Select

π = (circumference) / (diameter)

The first digits of π are 3.141592653589793238, but the digits go on forever.

For every circle
Circumference ÷ Diameter = π

The square root of a number that isn't a perfect square is also irrational. For example, √36 is a rational number, because 36 is the square of 6. But √37 is irrational, because 37 is not the square of an integer.

Check Your Understanding- Question 1 of 2
Identify each number as rational or irrational.
Number Type
4 1/3 Select
8 Select
√13 Select
√9 Select
π Select

Transcript text: 6:29 \[ \pi=\frac{\text { circumference }}{\text { diameter }} \] The first digits of $\pi$ are 3.141592653589793238 , but the digits go on forever. For every circles Circumference $\div$ Diameter $=\pi$ The square root of a number that isn't a perfect square is also irrational. For example, $\sqrt{36}$ is a rational number, because 36 is the square of 6 . But $\sqrt{37}$ is irrational, because 37 is not the square of an integer. Check Your Understanding- Question 1 of 2 Identify each number as rational or irrational. Number Type $4 \frac{1}{3}$ Select 8 Select .. $\sqrt{13}$ Select .. $\sqrt{9}$ Select .. $\pi$ Select .. HINT SUBMIT

Solution

Solution Steps

To determine whether each number is rational or irrational, we need to understand the definitions: a rational number can be expressed as a fraction of two integers, while an irrational number cannot. For each number, we will check if it can be expressed as a fraction or if it is a well-known irrational number.

$4 \frac{1}{3}$ is a mixed number, which can be converted to a fraction.
8 is an integer, which is a rational number.
$\sqrt{13}$ is not a perfect square, so it is irrational.
$\sqrt{9}$ is a perfect square, so it is rational.
$\pi$ is a well-known irrational number.

Step 1: Analyze $4 \frac{1}{3}$

The mixed number $4 \frac{1}{3}$ can be converted to an improper fraction: \[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \] Since it can be expressed as a fraction of two integers, $4 \frac{1}{3}$ is a rational number.

Step 2: Analyze $8$

The number $8$ is an integer. All integers can be expressed as a fraction (e.g., $8 = \frac{8}{1}$). Therefore, $8$ is a rational number.

Step 3: Analyze $\sqrt{13}$

The number $\sqrt{13}$ is not a perfect square, as $13$ does not have an integer square root. Thus, $\sqrt{13}$ is an irrational number.

Step 4: Analyze $\sqrt{9}$

The number $\sqrt{9}$ is equal to $3$, which is a perfect square. Since $3$ can be expressed as a fraction ($3 = \frac{3}{1}$), $\sqrt{9}$ is a rational number.

Step 5: Analyze $\pi$

The number $\pi$ is a well-known irrational number, as it cannot be expressed as a fraction of two integers.

Final Answer

$4 \frac{1}{3}$ is rational.
$8$ is rational.
$\sqrt{13}$ is irrational.
$\sqrt{9}$ is rational.
$\pi$ is irrational.

Thus, the classifications are:

$4 \frac{1}{3}$: Rational
$8$: Rational
$\sqrt{13}$: Irrational
$\sqrt{9}$: Rational
$\pi$: Irrational

The final answer is: \[ \boxed{ \begin{array}{ll} 4 \frac{1}{3} & \text{Rational} \\ 8 & \text{Rational} \\ \sqrt{13} & \text{Irrational} \\ \sqrt{9} & \text{Rational} \\ \pi & \text{Irrational} \end{array} } \]

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