Rational and Irrational Numbers in MYP Year 5
Understand rational and irrational numbers in MYP Year 5. Covers surds, decimal expansions, classification, and how these appear in MYP assessments.
Classifying Numbers
Every real number is either rational or irrational. A rational number can be expressed as a fraction p/q where p and q are integers and q ≠ 0. This includes all integers, terminating decimals, and recurring decimals. An irrational number cannot be written in this form — its decimal expansion is non-terminating and non-recurring.
Examples of Each
- Rational: ¾, −5, 0.6̄, 1.25
- Irrational: √2, π, √7, ∛3
Understanding Surds
Surds are irrational roots — square roots, cube roots, and higher roots that cannot be simplified to a rational number. In MYP Year 5, students must be able to:
- Identify whether a root is a surd (e.g. √9 = 3 is not a surd; √5 is)
- Simplify surds — e.g. √50 = 5√2
- Perform basic arithmetic with surds — adding like surds, multiplying surds
- Rationalise simple denominators — e.g. 1/√3 = √3/3
Decimal Expansions
Students are expected to recognise patterns in decimal expansions and use them to classify a number. Recurring decimals can always be converted to fractions using algebraic methods — a key technique assessed in Criterion A problems.
Common Misconceptions
- Assuming that all square roots are irrational — √16 = 4, which is rational
- Believing π = 22/7 exactly — this is only an approximation; π is irrational
- Confusing 'no exact decimal' with 'irrational' — all rationals have exact or recurring decimals
Where This Appears in MYP Assessment
Classification questions appear in short-answer formats under Criterion A. Surd simplification can appear in multi-step problems across algebra and geometry contexts. Understanding which answers should remain in surd form (exact values) versus decimal approximations is also important for Criterion C communication marks.