Grade 10 essential mathematics โ Real Numbers Quiz
1. Which of the following best describes the set of real numbers?
Real numbers include all rational numbers (integers, fractions, terminating/repeating decimals) and irrational numbers (non-terminating, non-repeating decimals).
2. Which type of number is โ2?
โ2 cannot be expressed as a ratio of two integers and has a non-terminating, non-repeating decimal expansion, so it is irrational.
3. Express 0.375 as a fraction in simplest form.
0.375 = 375/1000. Simplifying by dividing numerator and denominator by 125 gives 3/8.
4. What fraction is equal to 0.333... (repeating)?
0.333... repeating = 1/3 (because 1 รท 3 = 0.333...).
5. Which decimal expansion indicates an irrational number?
A non-terminating, non-repeating decimal expansion (like ฯ) represents an irrational number, while terminating or repeating decimals are rational.
6. Calculate -5 + 3.
-5 + 3 = -2 because adding a smaller positive number to a larger negative number moves the sum toward zero but remains negative.
7. Which of the following is NOT a rational number?
โ5 is not expressible as a ratio of two integers and has a non-terminating, non-repeating decimal expansion, so it is irrational.
8. Which number is an integer?
Integers are whole numbers and their negatives; -7 is an integer while the others are not whole numbers.
9. 0.142857142857... (repeating) is equal to which fraction?
0.142857 repeating is the decimal representation of 1/7.
10. Rationalise the denominator of 5/โ2 and give the result in simplest form.
Multiply numerator and denominator by โ2: (5/โ2) ร (โ2/โ2) = 5โ2/2.
11. Which set is NOT closed under subtraction?
Subtracting two natural numbers can give a non-natural result (e.g., 2 โ 5 = โ3), so natural numbers are not closed under subtraction; integers, rationals and reals are closed.
12. Which of the following is a surd (an irrational root left in root form)?
A surd is an irrational root kept in root form; โ3 is irrational and usually left as a surd.
13. Order the numbers from smallest to largest: -1, -0.75, 0.2, 0.5.
On the number line negatives are less than positives; among negatives, -1 < -0.75; positives 0.2 < 0.5, so the correct order is -1, -0.75, 0.2, 0.5.
14. What is the decimal form of 7/20?
7 รท 20 = 0.35 (move decimal two places because denominator 20 = 100/5).
15. Which of the following is NOT a real number?
2i is imaginary (involves the imaginary unit i = โโ1) and not a real number; the others are real.
16. Find the absolute value of โ3/4.
Absolute value removes the sign, so |โ3/4| = 3/4.
17. Which of the following fractions gives a terminating decimal?
A fraction in lowest terms has a terminating decimal if its denominator has only prime factors 2 and/or 5. 8 = 2^3 so 1/8 = 0.125 terminates.
18. Which statement is true about real numbers a and b with a < b?
Between any two distinct real numbers there are infinitely many rationals and irrationals; so there is at least one irrational between a and b.
19. If the product of two real numbers is zero, what can be concluded?
If ab = 0 for real numbers, then either a = 0 or b = 0 (or both).
20. Which fraction equals 0.222... (repeating)?
0.222... repeating = 2/9 because 2 รท 9 = 0.222...
21. Express โ50 in simplest surd form.
โ50 = โ(25ร2) = โ25 ร โ2 = 5โ2, which is the simplest surd form.
22. Which of the following has a non-terminating, non-repeating decimal expansion?
โ10 is irrational and so its decimal expansion is non-terminating and non-repeating; the others are rational with terminating decimals.
23. Convert 2.45 to a fraction in simplest form.
2.45 = 245/100. Simplify by dividing numerator and denominator by 5: 245/100 = 49/20.
24. Which inequality is true?
On the number line, -1/3 (โ -0.333) is to the right of -2/3 (โ -0.667), so -1/3 > -2/3.
25. Which of the following is an irrational number?
ฯ has a non-terminating, non-repeating decimal expansion and cannot be expressed as a ratio of integers, so it is irrational.