MYP3 Unit 1 – Indices and Algebraic Expressions 1.1 Define Rational Numbers (Vocabulary)

Vocabulary flashcards covering key concepts from the notes about rational numbers, irrational numbers, and related ideas.

Real Numbers

The set that includes both rational numbers and irrational numbers.

Natural Numbers

The set of counting numbers (1, 2, 3, …).

Whole Numbers

Natural numbers plus 0.

Integers

All whole numbers, including negatives: …, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

Rational Number

A number that can be written as a ratio of two integers; includes terminating and repeating decimals.

Irrational Number

A number that cannot be written as a ratio of two integers; decimal expansion is non-terminating and non-repeating.

Square Root

A number that, when multiplied by itself, yields the original number.

Radical Symbol

The symbol √ used to denote square roots.

Principal Square Root

The unique, non-negative (positive or zero) square root of a non-negative real number. For example, the principal square root of 9 is 3, not -3, and it is represented by the radical symbol √.

Perfect Square Number

A number that can be written as the product of two equal integers (n = k^2).

First 15 Perfect Squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

Terminating Decimal

A decimal that ends after a finite number of digits.

Repeating Decimal

A decimal with a repeating pattern after some point (non-terminating but repeating).

Counterexample to Lydia’s claim

Examples showing not all square roots are irrational, e.g., √4 = 2 and √9 = 3.

Product of Rational and Irrational

Usually irrational if the rational is nonzero; e.g., 2√2 is irrational; exception: 0 × √2 = 0 (rational).