Question

classify each number below as a rational number o (table with numbers 35.\overline{82}, \sqrt{17}, -6.37, -\sqrt{49}, -12\pi and columns rational, irrational with radio buttons)

Explanation:

Step1: Recall definitions

A rational number is a number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. It includes terminating decimals, repeating decimals, integers, fractions, etc. An irrational number is a number that cannot be expressed as a fraction of two integers and has a non - repeating, non - terminating decimal expansion.

Step2: Classify $35.\overline{82}$

A repeating decimal is a rational number because we can convert it into a fraction. Let $x = 35.\overline{82}=35.828282\cdots$. Then $100x=3582.8282\cdots$. Subtract $x$ from $100x$: $100x - x=3582.8282\cdots - 35.8282\cdots$, $99x = 3547$, $x=\frac{3547}{99}$. So $35.\overline{82}$ is rational.

Step3: Classify $\sqrt{17}$

17 is not a perfect square. The square root of a non - perfect square positive integer is an irrational number. So $\sqrt{17}$ is irrational.

Step4: Classify $- 6.37$

$-6.37$ is a terminating decimal. A terminating decimal can be written as a fraction (e.g., $-6.37=-\frac{637}{100}$). So $-6.37$ is rational.

Step5: Classify $-\sqrt{49}$

$\sqrt{49} = 7$, so $-\sqrt{49}=-7$. Integers are rational numbers (since $-7=\frac{-7}{1}$). So $-\sqrt{49}$ is rational.

Step6: Classify $-12\pi$

$\pi$ is an irrational number. The product of a non - zero rational number ($- 12$) and an irrational number ($\pi$) is an irrational number. So $-12\pi$ is irrational.

Answer:

• For $35.\overline{82}$: rational
• For $\sqrt{17}$: irrational
• For $-6.37$: rational
• For $-\sqrt{49}$: rational
• For $-12\pi$: irrational