Properties Of Rational And Irrational Numbers Worksheets [PDF]: Algebra 1 Math

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.

`1`. Fraction Form: Can be written as `\frac{a}{b}` with integers $a$ and $b \neq 0$.

`2`. Decimal Form: Terminates or repeats.

`1`. Can not be expressed as a fraction.

`2`. Decimal is non-terminating and non-repeating.

`1`. Rational: Terminating/repeating decimals, can be fractions.

`2`. Irrational: Non-terminating, non-repeating decimals.

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:

Identify Nature of $\sqrt{47}$ : $\sqrt{47}$ is the square root of a non-perfect square, which means it is an irrational number.
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 $t$ .
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. $\newline$
Final answer: Therefore, the statement that $t - \sqrt{47}$ can be rational or irrational, depending on the value of $t$ , is true.