Number Systems, Surds & Exponents is one of 9 topics in the Grade 10 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. Which of the following is a rational number?
0.25
2
π
5
Answer: 0.25 — 0.25 can be written as 41, a ratio of two integers, so it is rational. 2, π and 5 are all irrational.
Easy
2. What makes a number a surd rather than just any irrational number?
It is a root (such as a square root) that does not simplify to a whole number
It is any number greater than 10
It is always negative
It is any recurring decimal
Answer: It is a root (such as a square root) that does not simplify to a whole number — A surd is specifically an irrational root, like 2 or 5, that cannot be simplified to a whole number or exact fraction.
Medium
3. Convert the recurring decimal 0.6 (0.666...) into a fraction in simplest form.
Answer: 2/3 — Let x = 0.666..., so 10x = 6.666.... Subtracting: 9x = 6, so x = 6/9 = 2/3.
