Real Numbers — O/L Mathematics

What must I remember about Real Numbers?

• Real numbers (ℝ) comprise all Rational numbers (ℚ) and Irrational numbers (ℚ').
• Rational numbers can be expressed as a fraction p / q (p, q ∈ ℤ, q ≠ 0); their decimal representations are either terminating or non-terminating repeating (recurring).
• Irrational numbers cannot be written as p / q; their decimals are non-terminating and non-recurring (e.g., √2, √3, √5, π).
• Scientific notation (Standard form): Writing numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer.
• Approximating irrational roots: Estimating square roots of non-perfect squares to the first decimal place using consecutive perfect square bounds.

Test yourself (1 minute)

1. Standard form bound for A

   In A × 10ⁿ, A MUST satisfy 1 ≤ A < 10; writing 0.35 × 10⁴ or 35 × 10² is NOT valid standard form (must be 3.5 × 10³).

2. Negative exponents in standard form

   Numbers less than 1 have negative powers of 10 (e.g., 0.0048 = 4.8 × 10⁻³).

3. Rational vs Irrational identification

   √16 = 4 is rational; √8 = 2√2 is irrational; repeating decimals like 0.333... = 1/3 are rational.

Practise Real Numbers questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 1)

What comes next?

Next in the syllabus

Where does Real Numbers fit in the syllabus?

Grade 11 · Term 1