Number System Case Study Questions Class 9

number system case study questions class 9 | Free Online Test

Number System Case Study Questions Class 9: Introduction

Students preparing for exams often search for Case Study math questions for class 9. These exercises help strengthen concepts in the number system. Our online tests include interactive math case study questions class 9 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 Math Case Study Questions Class 9

Math case study questions class 9 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 9 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 2: Decimal Representations of Rational Numbers

Rajeev was studying decimal representations of rational numbers. His teacher asked him to convert $\dfrac{1}{4}$ and $\dfrac{1}{3}$ into decimal form. Rajeev observed that $\dfrac{1}{4} = 0.25$ terminates, while $\dfrac{1}{3} = 0.333\ldots$ continues forever in a pattern. His friend Ritu added that this is how we classify rational numbers into terminating and non-terminating recurring decimals. She asked if there is a rule to predict whether a given fraction will terminate or not.

Which of the following statements correctly predicts whether a decimal will terminate?

  • A) A decimal terminates if the denominator has only 2 and 5 as prime factors.
  • B) A decimal terminates if the numerator is smaller than the denominator.
  • C) A decimal terminates if the number is greater than 1.
  • D) A decimal always terminates if it’s a proper fraction.
Answer: A) A decimal terminates if the denominator has only 2 and 5 as prime factors.
Explanation: A rational number in lowest terms will have a terminating decimal expansion only if the denominator has no prime factors other than 2 and 5.

1. Which of the following fractions will have a terminating decimal expansion?

  • A) $\dfrac{3}{8}$
  • B) $\dfrac{2}{11}$
  • C) $\dfrac{7}{6}$
  • D) $\dfrac{5}{7}$
Answer: A) $\dfrac{3}{8}$
Explanation: $\dfrac{3}{8}$ has denominator $8 = 2^3$, which contains only 2 as a prime factor. So the decimal terminates.

2. What is the decimal expansion of $\dfrac{7}{20}$?

  • A) $0.36$
  • B) $0.35$
  • C) $0.375$
  • D) $0.385$
Answer: C) $0.375$
Explanation: $\dfrac{7}{20} = 0.375$, which is terminating since $20 = 2^2 \times 5$.

3. Which of the following will result in a non-terminating repeating decimal?

  • A) $\dfrac{5}{25}$
  • B) $\dfrac{1}{40}$
  • C) $\dfrac{7}{12}$
  • D) $\dfrac{3}{8}$
Answer: C) $\dfrac{7}{12}$
Explanation: $\dfrac{7}{12} = 0.58\overline{3}$, non-terminating repeating decimal, since 12 has 3 as a prime factor.

4. Which condition guarantees a terminating decimal representation for a rational number $\dfrac{p}{q}$ in lowest terms?

  • A) $q$ has only 2 and/or 5 as prime factors.
  • B) $p$ and $q$ are both even.
  • C) $q$ is less than $p$.
  • D) $q$ is a multiple of 10.
Answer: A) $q$ has only 2 and/or 5 as prime factors.
Explanation: The decimal of $\dfrac{p}{q}$ terminates only when $q$ in lowest form has no prime factors other than 2 or 5.

5. Which among the following has a terminating decimal representation?

  • A) $\dfrac{4}{15}$
  • B) $\dfrac{11}{40}$
  • C) $\dfrac{7}{33}$
  • D) $\dfrac{9}{14}$
Answer: B) $\dfrac{11}{40}$
Explanation: $\dfrac{11}{40}$ terminates since $40 = 2^3 \times 5$. All prime factors are 2 and 5 only.

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