Eighth Grade Rational and Irrational Numbers Quiz - Twinkl - Free Printable

Problem: Solving the "Rational and Irrational Numbers Quiz"

The quiz consists of four main sections. Let's solve each section step by step.

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Section 1: Write each decimal below as a fraction in simplest form.

#### a. -2.498
- Convert the decimal to a fraction:
\[
-2.498 = -\frac{2498}{1000}
\]
- Simplify the fraction by finding the greatest common divisor (GCD) of 2498 and 1000. The GCD is 2.
\[
-\frac{2498 \div 2}{1000 \div 2} = -\frac{1249}{500}
\]
- Final answer:
\[
-\frac{1249}{500}
\]

#### b. 0.12
- Convert the decimal to a fraction:
\[
0.12 = \frac{12}{100}
\]
- Simplify the fraction by finding the GCD of 12 and 100. The GCD is 4.
\[
\frac{12 \div 4}{100 \div 4} = \frac{3}{25}
\]
- Final answer:
\[
\frac{3}{25}
\]

---

Section 2: Write each fraction as a decimal.

#### a. \(\frac{17}{2}\)
- Perform the division:
\[
\frac{17}{2} = 8.5
\]
- Final answer:
\[
8.5
\]

#### b. \(\frac{7}{100}\)
- Perform the division:
\[
\frac{7}{100} = 0.07
\]
- Final answer:
\[
0.07
\]

---

Section 3: Determine if each number is rational or irrational by placing a checkmark in the corresponding box.

#### a. \(4\pi\)
- \(\pi\) is an irrational number, and multiplying it by a rational number (4) results in an irrational number.
- Irrational

#### b. \(\frac{5}{7}\)
- This is a ratio of two integers, so it is a rational number.
- Rational

#### c. \(0.25\pi\)
- \(\pi\) is an irrational number, and multiplying it by a rational number (0.25) results in an irrational number.
- Irrational

#### d. \(-3.287875321...\)
- This number has a non-repeating, non-terminating decimal expansion, which means it is irrational.
- Irrational

#### e. \(\sqrt{81}\)
- Simplify the square root:
\[
\sqrt{81} = 9
\]
- 9 is a rational number.
- Rational

#### f. \(\overline{7.121}\)
- The bar over \(7.121\) indicates a repeating decimal (\(7.121121121...\)).
- Repeating decimals are rational numbers.
- Rational

---

Section 4: Circle all the rational numbers.

#### a. \(4\pi\)
- As explained earlier, \(4\pi\) is irrational.

#### b. \(\frac{5}{7}\)
- This is a rational number.

#### c. \(0.25\pi\)
- As explained earlier, \(0.25\pi\) is irrational.

#### d. \(-3.287875321...\)
- As explained earlier, this is an irrational number.

#### e. \(\sqrt{81}\)
- As explained earlier, \(\sqrt{81} = 9\), which is rational.

#### f. \(\overline{7.121}\)
- As explained earlier, this is a rational number.

- Rational numbers: \(\frac{5}{7}\), \(\sqrt{81}\), \(\overline{7.121}\)

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Final Answers:

1. Section 1:
- a. \(\boxed{-\frac{1249}{500}}\)
- b. \(\boxed{\frac{3}{25}}\)

2. Section 2:
- a. \(\boxed{8.5}\)
- b. \(\boxed{0.07}\)

3. Section 3:
- a. Irrational
- b. Rational
- c. Irrational
- d. Irrational
- e. Rational
- f. Rational

4. Section 4:
- Circle: \(\frac{5}{7}\), \(\sqrt{81}\), \(\overline{7.121}\)

---

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
&\text{Section 1:} & \text{a. } -\frac{1249}{500}, & \text{b. } \frac{3}{25} \\
&\text{Section 2:} & \text{a. } 8.5, & \text{b. } 0.07 \\
&\text{Section 3:} & \text{a. Irrational, b. Rational, c. Irrational, d. Irrational, e. Rational, f. Rational} \\
&\text{Section 4:} & \text{Circle: } \frac{5}{7}, \sqrt{81}, \overline{7.121}
\end{aligned}
}
\]