Practice Questions on Real Number System

Practice Questions Instructions

• Circle the correct answer: A, B, C, D, or E

Topic 1: Real Number System

Question 1: Membership in Number Sets

• Problem: Determine which two number sets include the number (-\frac{3}{5}).

• Options:

  • A) Irrational, Integer

  • B) Rational, Integer

  • C) Irrational, Real

  • D) Rational, Real

  • E) none of the above

• Correct Answer: D) Rational, Real

  • Explanation:

  • (-\frac{3}{5}) is a fraction, hence it's a rational number.

  • All rational numbers are part of the real number set.

Question 2: Truth Statements about Numbers

• Problem: Identify which statement is true.

• Options:

  • A) If a number is an integer, then it is also rational.

  • B) All integers are whole numbers.

  • C) The number (2\pi) is rational.

  • D) Some numbers are both rational and irrational.

  • E) none of the above

• Correct Answer: A) If a number is an integer, then it is also rational.

  • Explanation:

  • Integers can be expressed as a fraction (e.g., (3 = \frac{3}{1})), confirming they are rational.

Question 3: Identifying Numbers within a Range

• Problem: Which real number lies between 4 and 4.5?

• Options:

  • A) (-\sqrt[4]{20})

  • B) (\sqrt{15})

  • C) 4

  • D) (\frac{17}{4})

  • E) none of the above

• Correct Answer: B) (\sqrt{15})

  • Explanation:

  • (\sqrt{15} \approx 3.872), which is not between 4 and 4.5.

  • Unavailable options yield (4.25) or neither of these values.

Summary of Key Concepts

• The Real Number System is comprised of rational and irrational numbers.

• Rational numbers can be represented as a fraction (\frac{p}{q}), where p and q are integers and q ≠ 0.

• Irrational numbers cannot be expressed as fractions and include numbers like (\pi) and (\sqrt{2}).

• A number is rational if it can be expressed as a fraction, and every integer falls into this category.

• Important to understand the classification and properties of numbers in exams.