Lesson 1: Rational Numbers and Decimal Expansions — Practice Questions

1. 1. Which of the following numbers is an irrational number?

   • A. $0.25$
   • B. $0.\overline{3}$
   • C. $4.121314...$
   • D. $6.0$

2. 2. The fraction $\frac{5}{8}$ is a rational number. Its decimal form is $0.625$. Because the decimal ends, it is known as a ___ decimal.

3. 3. Which decimal is equivalent to the rational number written as $0.\overline{15}$?

   • A. $0.151515...$
   • B. $0.1555...$
   • C. $0.15$
   • D. $0.115115...$

4. 4. The decimal representation of the rational number $\frac{4}{9}$ is $0.444...$. This type of decimal is called a ___ decimal.

5. 5. Which statement best describes the number $7.12345...$, where the digits continue forever without any repeating pattern?

   • A. The number is rational because it is a decimal.
   • B. The number is irrational because its decimal is non-terminating and non-repeating.
   • C. The number is rational because all decimals are rational.
   • D. The number is a terminating decimal.

6. 6. To convert a rational number to a decimal, use long division. What is the decimal form of the fraction $\frac{3}{8}$? Answer: ___

7. 7. When converting an improper fraction to a decimal, the process is the same. What is the decimal equivalent of the fraction $\frac{13}{5}$?

   • A. 2.6
   • B. 2.5
   • C. 1.35
   • D. 2.3

8. 8. When converting a fraction to a decimal using long division, what causes the decimal to be a repeating decimal?

   • A. A non-zero remainder repeats
   • B. The remainder eventually becomes 0
   • C. The numerator is an odd number
   • D. The denominator is larger than the numerator

9. 9. Some fractions result in repeating decimals. What is the decimal form of $\frac{4}{9}$? Write the first four decimal places. Answer: ___

10. 10. What is the decimal representation of the rational number $\frac{5}{6}$?

    • A. 0.8333...
    • B. 0.83
    • C. 0.56
    • D. 0.8