# 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
Show all

## Solved Example

Q. The number $t$ is irrational. Which statement about $t - \sqrt{47}$ is true?$\newline$Choices:$\newline$(A) $t - \sqrt{47}$ is rational. $\newline$(B) $t - \sqrt{47}$ is irrational. $\newline$(C) $t - \sqrt{47}$ can be rational or irrational, depending on the value of $t$.
Solution:
1. Identify Nature of $\sqrt{47}$: $\sqrt{47}$ 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.$\newline$The difference between two irrational numbers can be either rational or irrational. It is not possible to determine the nature of $t - \sqrt{47}$ without knowing the specific value of $t$.
3. Analyze Given Choices: Analyze the given choices in relation to the subtraction of irrational numbers. $\newline$If $t$ were specifically chosen to be $\sqrt{47}$, then $t - \sqrt{47}$ would be $0$, which is rational. $\newline$However, if $t$ is any other irrational number, $t - \sqrt{47}$ could still be irrational. $\newline$
4. Final answer: Therefore, the statement that $t - \sqrt{47}$ can be rational or irrational, depending on the value of $t$, is true.

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”