Case Study on Number System Class 10

Case Study on Number System Class 10 | Free Online Test

Case Study on Number System Class 10

Students preparing for exams often search for Case Study math questions for class 10. These exercises help strengthen concepts in the number system. Our online tests include interactive math case study questions class 10 that focus on real-life applications of numbers. Practicing these questions regularly improves accuracy and speed. Additionally, students develop problem-solving skills while applying formulas in practical situations.

Importance of Case Study on Number System Class 10

Math case study questions class 10 encourage analytical thinking and logical reasoning. For instance, questions on rational and irrational numbers allow deeper understanding. Furthermore, solving these problems enhances critical thinking. Short exercises help reinforce key formulas. Therefore, students gain confidence and clarity in the number system through consistent practice.

Benefits of Online Test Practice

Our math case study questions online tests provide instant feedback and performance tracking. Students can identify errors quickly and improve their approach. The number system case study questions class 10 cover various difficulty levels. Consequently, learners strengthen concepts efficiently and are better prepared for exams. Regular practice ensures mastery of fundamental number system topics.

Case Study: Understanding Irrational Numbers

Case Study 2: Understanding Irrational Numbers

Priya is curious about irrational numbers and wants to understand why certain numbers like \(\sqrt{2}\) and \(\pi\) cannot be written in the form \(\frac{p}{q}\). She starts testing their decimal expansions and realizes they never terminate or repeat. She uses this knowledge in her math club activities to challenge her friends with identifying irrational numbers from a list.

Key concepts:

  • A rational number can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\)
  • An irrational number cannot be expressed as a simple fraction
  • The decimal expansion of a rational number either terminates or repeats
  • The decimal expansion of an irrational number is non-terminating and non-repeating
  • Examples of irrational numbers include \(\sqrt{2}\), \(\sqrt{3}\), \(\pi\), and \(e\)

1. Which of the following is an irrational number?

  • A) \(\frac{4}{7}\)
  • B) \(0.121212\ldots\)
  • C) \(\sqrt{3}\)
  • D) \(1.25\)
Answer: C) \(\sqrt{3}\)
Solution: \(\sqrt{3}\) is not a perfect square and has a non-terminating, non-repeating decimal.

2. What is the nature of the decimal expansion of \(\frac{22}{7}\)?

  • A) Terminating
  • B) Non-terminating, repeating
  • C) Non-terminating, non-repeating
  • D) Whole number
Answer: B) Non-terminating, repeating
Solution: \(\frac{22}{7} = 3.142857142857\ldots\), repeating block “142857”

3. Which statement is true?

  • A) All rational numbers are integers
  • B) All irrational numbers are real numbers
  • C) All real numbers are irrational
  • D) All integers are irrational
Answer: B) All irrational numbers are real numbers
Solution: Real numbers include both rational and irrational numbers.

4. Identify the number with a terminating decimal expansion.

  • A) \(\frac{5}{16}\)
  • B) \(\frac{7}{9}\)
  • C) \(\frac{11}{6}\)
  • D) \(\frac{10}{3}\)
Answer: A) \(\frac{5}{16}\)
Solution: Denominator is \(2^4\), so decimal terminates.

5. Which of these is not a rational number?

  • A) \(0.666\ldots\)
  • B) \(\sqrt{5}\)
  • C) \(\frac{7}{8}\)
  • D) \(-3\)
Answer: B) \(\sqrt{5}\)
Solution: \(\sqrt{5}\) is irrational as it cannot be expressed as \(\frac{p}{q}\).

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