Topic 2 Test Review: Rational & Irrational Numbers

Vocabulary and practice flashcards covering Rational and Irrational Numbers, including decimal classifications and conversion steps.

Rational Number

A number that can be written as a fraction.

Irrational Number

A decimal that goes on forever without repeating.

Repeating Decimal

A decimal with digits that repeat in a pattern.

Terminating Decimal

A decimal that ends.

Classification of $0.5$

Rational number, because it is a terminating decimal.

Classification of $∓$ equation $\sqrt{3} = 1.732050808...$

Irrational number, because it is a decimal that goes on forever without repeating.

Classification of $0.888...$

Rational number, because it is a repeating decimal.

Classification of $\pi$ (pi)

Irrational number, because it goes on forever without repeating.

Step 1: Converting Repeating Decimals to Fractions

Let $x = \text{repeating decimal}$.

Step 2: Converting Repeating Decimals to Fractions

Multiply both sides by $10$ (or $100$ if $2$ digits repeat).

Step 3: Converting Repeating Decimals to Fractions

Subtract the original equation.

Step 4: Converting Repeating Decimals to Fractions

Solve for $x$.

Step 5: Converting Repeating Decimals to Fractions

Simplify the fraction.

Conversion of $0.272727...$ to a Fraction

Multiply by $100$ to get $100x = 27.2727...$, subtract $x$ to get $99x = 27$, and simplify to $x = \frac{27}{99} = \frac{3}{11}$.

Classification of $\sqrt{9}$

Rational number, because $\sqrt{9} = 3$.

Classification of $\sqrt{5}$

Irrational number, because $5$ is not a perfect square and its decimal goes on forever without repeating.

Classification of $0.123456789...$

Irrational number, because it goes on forever without repeating.