Properties Of Rational And Irrational Numbers Worksheet

6 problems

Properties of rational and irrational numbers:

Rational Numbers: Can be expressed as a fraction `\frac{a}{b}` where \(a\) and \(b\) are integers, and \(b \neq 0\). They have either terminating or repeating decimal expansions.

Irrational Numbers: Cannot be expressed as a simple fraction. Their decimal expansions are non-terminating and non-repeating. Examples include \(\sqrt{2}\), \(\pi\), and \(e\). They fill the gaps between rational numbers on the number line.

Algebra 1
Algebra Foundations

How Will This Worksheet on "Properties of Rational and Irrational Numbers" Benefit Your Students' Learning?

  • Improving knowledge of number classification.
  • Using practice problems to reinforce concepts.
  • Gaining the ability to recognize and distinguish between irrational and rational numbers.
  • Developing the capacity to solve problems.
  • Getting pupils ready for complex mathematical ideas.
  • Gaining assurance when working with different kinds of numbers.
  • Offering a strong basis for algebra and other advanced mathematics.

How to Find Properties of Rational and Irrational Numbers?

  • Determine if it's a fraction, integer, decimal, or
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Solved Example

Q. The number t t is irrational. Which statement about t47 t - \sqrt{47} is true?\newlineChoices:\newline(A) t47 t - \sqrt{47} is rational. \newline(B) t47 t - \sqrt{47} is irrational. \newline(C) t47 t - \sqrt{47} can be rational or irrational, depending on the value of t t .
Solution:
  1. Identify Nature of 47\sqrt{47}: 47\sqrt{47} is the square root of a non-perfect square, which means it is an irrational number.
  2. Consider Subtraction of Irrational Numbers: Consider the subtraction of two irrational numbers.\newlineThe difference between two irrational numbers can be either rational or irrational. It is not possible to determine the nature of t47t - \sqrt{47} without knowing the specific value of tt.
  3. Analyze Given Choices: Analyze the given choices in relation to the subtraction of irrational numbers. \newlineIf tt were specifically chosen to be 47\sqrt{47}, then t47t - \sqrt{47} would be 00, which is rational. \newlineHowever, if tt is any other irrational number, t47t - \sqrt{47} could still be irrational. \newline
  4. Final answer: Therefore, the statement that t47t - \sqrt{47} can be rational or irrational, depending on the value of tt, is true.

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