Number System Blog Post - Interactive Worksheets & Quizzes

Number System

Overview

This blog post explores the Number System, covering real numbers and complex numbers. Below you will find detailed sections on Rational and Irrational Numbers, along with interactive worksheets and quizzes to test your knowledge.

Real Numbers

Complex Numbers

Real Numbers

  • Rational Numbers
  • Irrational Numbers

Rational Numbers

Numbers written in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \), are known as Rational numbers.

Example:

\( \frac{3}{5}, \; \frac{22}{7}, \; 0, \; -5 \) are rational numbers.

Terminating and non-terminating but repeating decimals are also considered rational numbers.

Example:

\( 2.256 \) is a terminating decimal, so it’s a rational number.
(NOTE: A terminating decimal has a finite number of digits after the decimal point.)
\( 0.333... \) is a non-terminating but repeating decimal, so it is a rational number.
(NOTE: A non-terminating repeating decimal has some digits that repeat infinitely.)

Irrational Numbers

In this section, we will complete all topics on the Number System with examples, and then move on to interactive worksheets and quizzes.

Explore Worksheet Section

Beginner Level Worksheet

  • Worksheet 1: Introduction to the Number System

    Solve: Calculate \( \frac{2}{3} + \frac{1}{3} \).

    Answer: \( \frac{2}{3} + \frac{1}{3} = 1 \)

  • Worksheet 2: Basic Rational and Irrational Numbers

    Task: Identify whether \( \sqrt{2} \) is a rational or irrational number.

    Answer: \( \sqrt{2} \) is an irrational number.

Intermediate Level Worksheet

  • Worksheet 3: Operations on Rational Numbers

    Solve: \( \frac{5}{8} - \frac{3}{8} \).

    Answer: \( \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \)

  • Worksheet 4: Advanced Rational and Irrational Numbers

    Task: Determine if \( 0.121212... \) is a rational number.

    Answer: \( 0.121212... \) is rational because it is a repeating decimal.

Advanced Level Worksheet

  • Worksheet 5: Complex Applications in Number System

    Challenge: Explain the differences between rational and irrational numbers with examples.

    Answer: Rational numbers can be expressed as a fraction of integers. In contrast, irrational numbers cannot be so expressed. For example, \( \frac{3}{5} \) is rational while \( \sqrt{2} \) is irrational.

  • Worksheet 6: Deep Dive into Number Theory

    Task: Provide an example of a number that is both irrational and transcendental.

    Answer: \( \pi \) is both irrational and transcendental.

Quiz Section

Beginner Level Quiz

Question 1: What is the value of \( \frac{2}{3} + \frac{1}{3} \)?

Question 2: Which of the following numbers is irrational?

Intermediate Level Quiz

Question 3: What is \( \frac{5}{8} - \frac{3}{8} \)?

Question 4: \( 0.121212... \) is a repeating decimal. Is it rational?

Advanced Level Quiz

Question 5: Which number is known to be both irrational and transcendental?

Question 6: Explain in short why \( \sqrt{2} \) is irrational.


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