201. Write 0.overline45 as a fraction in lowest terms.
- 511
- 12
- 4699
- 920
Answer: A) 511
Explanation: Let x = 0.overline45. Then 100x = 45.overline45, so 99x = 45 and x = 4599 = 511. SLO M-09-A-02 · Knowledge
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 9)
230 multiple-choice questions on Real Numbers from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
202. Given log 2 = 0.3010 and log 3 = 0.4771, find log 9.
- 0.8781
- 0.9542
- 1.2552
- 0.1436
Answer: B) 0.9542
Explanation: log 9 = 2log 3 = 0.9542. SLO M-09-A-08 · Application
203. Which of the following is a rational number?
- [3]5
- 15
- 227
- 50
Answer: C) 227
Explanation: 227 can be written as pq with q neq 0, so it is rational. The others are irrational. SLO M-09-A-02 · Knowledge
204. Find log2 32.
- 6
- 10
- 5
- -5
Answer: C) 5
Explanation: log2 x = y means 2^y = x. Since 2^5 = 32, the answer is 5. SLO M-09-A-06 · Knowledge
205. Write 3^4 = 81 in logarithmic form.
- log3 4 = 81
- log81 3 = 4
- log3 81 = 4
- log4 81 = 3
Answer: C) log3 81 = 4
Explanation: a^y = x iff loga x = y. So 3^4 = 81 becomes log3 81 = 4. SLO M-09-A-06 · Knowledge
206. Find log4 2.
- 1
- 32
- 12
- - 12
Answer: C) 12
Explanation: log4 x = y means 4^y = x. Since 4^ 12 = 2, the answer is 12. SLO M-09-A-06 · Knowledge
207. Write 7.7 10^-4 as an ordinary number.
- 77,000
- 0.000077
- 0.0077
- 0.00077
Answer: D) 0.00077
Explanation: Move the decimal point 4 places to the left: 0.00077. SLO M-09-A-05 · Understanding
208. Find log8 4.
- 43
- 53
- - 23
- 23
Answer: D) 23
Explanation: log8 x = y means 8^y = x. Since 8^ 23 = 4, the answer is 23. SLO M-09-A-06 · Knowledge
209. A shopkeeper buys a watch for Rs. 1,250 and sells it for Rs. 1,500. His profit percentage is:
- 20%
- 16.67%
- 250%
- 25%
Answer: A) 20%
Explanation: Profit = 1500 - 1250 = 250. Profit % = 2501250 100 = 20% (always on cost price). SLO M-09-A-09 · Application
210. The Sumerians and Babylonians wrote numbers in a system with base:
- 60
- 20
- 10
- 12
Answer: A) 60
Explanation: The Sumerians, and later the Babylonians, used a sexagesimal (base-60) system, written in cuneiform on clay tablets. SLO M-09-A-01 · Knowledge
211. The diameter of a red blood cell is about 0.000,007 m. In scientific notation this is:
- 7 10^-6 m
- 0.7 10^-5 m
- 7 10^-5 m
- 7 10^6 m
Answer: A) 7 10^-6 m
Explanation: Move the decimal point 6 places right to reach 7, so the power is -6. SLO M-09-A-05 · Understanding
212. A bank pays a profit of 14% per year on savings. Profit on Rs. 75,000 for one year is:
- Rs. 11,500
- Rs. 105,000
- Rs. 10,500
- Rs. 5357.14
Answer: C) Rs. 10,500
Explanation: Profit = 14100 75000 = 10500. SLO M-09-A-09 · Application
213. 227 is:
- an irrational number
- a rational approximation of pi
- not a real number
- exactly equal to pi
Answer: B) a rational approximation of pi
Explanation: 227 = 3.overline142857 is rational; pi = 3.14159ldots is irrational, so 227 is only an approximation. SLO M-09-A-02 · Knowledge
214. If logx 243 = 5, then x =
- 2
- 15
- 4
- 3
Answer: D) 3
Explanation: x^5 = 243, so x = [5]243 = 3. SLO M-09-A-06 · Knowledge
215. Calculate (3 10^4) (2 10^5).
- 6 10^1
- 6 10^20
- 6 10^9
- 5 10^9
Answer: C) 6 10^9
Explanation: Multiply the numbers and add the powers: 3 2 = 6 and 10^4+5 = 10^9. SLO M-09-A-05 · Understanding
216. The number 46 written in Roman numerals is:
- XLVI
- XLVII
- LVI
- XLVIII
Answer: A) XLVI
Explanation: Write each place separately: 46 to XLVI. SLO M-09-A-01 · Knowledge
217. Simplify 3 2 + 5 8.
- 13 2
- 14 2
- 8 4
- 8 8
Answer: A) 13 2
Explanation: 8 = 2 2, so the sum is 3 2 + 10 2 = 13 2. SLO M-09-A-04 · Application
218. Ancient Chinese mathematicians used red and black counting rods to show:
- prime and composite numbers
- fractions and decimals
- positive and negative numbers
- even and odd numbers
Answer: C) positive and negative numbers
Explanation: Red rods stood for positive and black rods for negative numbers — one of the earliest uses of negative numbers. SLO M-09-A-01 · Knowledge
219. A family earns Rs. 45,000 a month. It spends 15 on rent and 12 on food. How much is left?
- Rs. 40,500
- Rs. 22,500
- Rs. 9,000
- Rs. 13,500
Answer: D) Rs. 13,500
Explanation: Fraction left = 1 - 15 - 12 = 310, and 310 45000 = 13500. SLO M-09-A-09 · Application
220. The year 2026 written in Roman numerals is:
- MMXXVIII
- MMXXVI
- MMXXVII
- MMXXXVI
Answer: B) MMXXVI
Explanation: Write each place separately: 2026 to MMXXVI. SLO M-09-A-01 · Knowledge
221. ln x means the same as:
- log10 x
- loge x
- logx e
- e^x
Answer: B) loge x
Explanation: ln is short for the logarithm to base e. SLO M-09-A-07 · Knowledge
222. Which number is written correctly in scientific notation?
- 45 10^5
- 4.5 10^6
- 0.45 10^7
- 4.5 100^3
Answer: B) 4.5 10^6
Explanation: In scientific notation a 10^n we need 1 le a < 10 and n an integer. SLO M-09-A-05 · Understanding
223. Simplify log 50 - log 5.
- log 45
- 0
- log 10.5
- 1
Answer: D) 1
Explanation: Combine with the laws of logarithms: sums become products, differences become quotients, and log 10 = 1. SLO M-09-A-08 · Application
224. The Hindu–Arabic numerals were made popular in Europe by Fibonacci in his book:
- Al-Jabr
- Elements
- Principia
- Liber Abaci (1202)
Answer: D) Liber Abaci (1202)
Explanation: Leonardo of Pisa (Fibonacci) learnt the numerals in North Africa and explained them in Liber Abaci (1202). SLO M-09-A-01 · Knowledge
225. Which property is shown by if x = y then 11x = 11y?
- Multiplicative identity
- Multiplicative property of equality
- Multiplicative inverse
- Commutative property of addition
Answer: B) Multiplicative property of equality
Explanation: if x = y then 11x = 11y is the multiplicative property of equality. SLO M-09-A-03 · Knowledge