51. log 1000 =
- 4
- 3
- -3
- 2
Answer: B) 3
Explanation: 1000 = 10^3, so log 1000 = 3. SLO M-09-A-07 · Knowledge
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 3)
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.
52. Write 0.2overline3 as a fraction in lowest terms.
- 23100
- 2390
- 2399
- 730
Answer: D) 730
Explanation: Let x = 0.2overline3. Then 100x - 10x = 23 - 2 = 21, so x = 2190 = 730. SLO M-09-A-02 · Knowledge
53. Simplify 2log 3 + log 4.
- log 24
- log 12
- log 36
- log 10
Answer: C) log 36
Explanation: Combine with the laws of logarithms: sums become products, differences become quotients, and log 10 = 1. SLO M-09-A-08 · Application
54. Which of the following is an irrational number?
- 2
- 1625
- 0.75
- 0.overline3
Answer: A) 2
Explanation: 2 is irrational because 2 is not a perfect square. The others can be written as pq (e.g. 49 = 7, 0.overline3 = 13). SLO M-09-A-02 · Knowledge
55. Write 0.overline81 as a fraction in lowest terms.
- 911
- 910
- 81100
- 8299
Answer: A) 911
Explanation: Let x = 0.overline81. Then 100x = 81.overline81, so 99x = 81 and x = 8199 = 911. SLO M-09-A-02 · Knowledge
56. The earliest way people recorded counts (e.g. on the Ishango bone) was:
- fractions
- place-value numerals
- tally marks
- Roman numerals
Answer: C) tally marks
Explanation: Prehistoric people cut tally marks on bones and sticks — one mark for each object counted. SLO M-09-A-01 · Knowledge
57. Given log 2 = 0.3010 and log 3 = 0.4771, find log 0.6.
- -0.2219
- 0.0791
- 0.8781
- 0.1436
Answer: A) -0.2219
Explanation: log 0.6 = log 2 + log 3 - log 10 = -0.2219. SLO M-09-A-08 · Application
58. In the Babylonian base-60 system, a number written as 1 sixties and 40 ones equals:
- 50
- 140
- 20
- 100
Answer: D) 100
Explanation: Each place is worth 60 times the one to its right: 1 60 + 40 = 100. SLO M-09-A-01 · Knowledge
59. Sound level is L = 10 log ( II0 ) decibels. A sound 1,000,000 times as intense as I0 has a level of:
- 600 dB
- 6 dB
- 60 dB
- 70 dB
Answer: C) 60 dB
Explanation: L = 10 log 10^6 = 10 6 = 60 dB. SLO M-09-A-08 · Application
60. The characteristic of log 0.45 is:
- 5
- bar1
- 0
- 3
Answer: B) bar1
Explanation: For a number ge 1 the characteristic is one less than the number of digits before the decimal point; for a number < 1 it is negative — one more than the number of zeros right after the decimal point (written with a bar). SLO M-09-A-07 · Knowledge
61. Which ancient system had no symbol for zero and no place value?
- Roman numerals
- Modern decimal numerals
- Mayan numerals
- Hindu–Arabic numerals
Answer: A) Roman numerals
Explanation: Roman numerals (I, V, X, L, C, D, M) are added and subtracted; there is no zero and no place value, which makes calculation slow. SLO M-09-A-01 · Knowledge
62. Solve 2^x = 32 using logarithms.
- x = 4
- x = 5
- x = 6
- x = 16
Answer: B) x = 5
Explanation: x = log 32log 2 = 5log 2log 2 = 5. SLO M-09-A-08 · Application
63. The ancient Egyptian hieroglyphic number system was:
- base 20 with a zero
- base 60 with place value
- base 10, with a separate symbol for each power of 10 and no place value
- base 2 with a zero
Answer: C) base 10, with a separate symbol for each power of 10 and no place value
Explanation: Egyptians repeated symbols for 1, 10, 100, 1000, ldots and added them up — base 10, but with no place value and no zero. SLO M-09-A-01 · Knowledge
64. Which property is shown by if x = y and y = 10 then x = 10?
- Commutative property of addition
- Transitive property of equality
- Commutative property of multiplication
- Transitive property of inequality
Answer: B) Transitive property of equality
Explanation: if x = y and y = 10 then x = 10 is the transitive property of equality. SLO M-09-A-03 · Knowledge
65. The value of e, correct to 3 decimal places, is:
- 2.718
- 3.142
- 2.303
- 1.414
Answer: A) 2.718
Explanation: e = 2.71828ldots is an irrational number. SLO M-09-A-07 · Knowledge
66. Evaluate 1000^ 23.
- 1100
- 100
- 20003
- 1000
Answer: B) 100
Explanation: 1000 = 10^3, so 1000^ 23 = (10^3 )^ 23 = 10^2 = 100. SLO M-09-A-04 · Application
67. On the Richter scale M = log AA0. An earthquake of magnitude 7 has an amplitude how many times that of a magnitude-5 earthquake?
- 1.4 times
- 20 times
- 2 times
- 100 times
Answer: D) 100 times
Explanation: A difference of 2 in magnitude means log A1A2 = 2, i.e. 10^2 = 100 times. SLO M-09-A-08 · Application
68. Write 0.000000125 in scientific notation.
- 1.25 10^-8
- 1.25 10^7
- 1.25 10^-7
- 1.25 10^-6
Answer: C) 1.25 10^-7
Explanation: Move the decimal point so that one non-zero digit is before it: 0.000000125 = 1.25 10^-7 (right by 7 places). SLO M-09-A-05 · Understanding
69. Write 1,800,000 in scientific notation.
- 1.8 10^5
- 1.8 10^-6
- 1.8 10^7
- 1.8 10^6
Answer: D) 1.8 10^6
Explanation: Move the decimal point so that one non-zero digit is before it: 1,800,000 = 1.8 10^6 (left by 6 places). SLO M-09-A-05 · Understanding
70. e^ln 7 =
- 7
- 1
- ln 7
- e^7
Answer: A) 7
Explanation: e^x and ln x undo each other, so e^ln 7 = 7. SLO M-09-A-07 · Knowledge
71. log10(-100) is:
- -2
- not defined (no real value)
- -100
- 2
Answer: B) not defined (no real value)
Explanation: A positive base raised to any real power is always positive, so the logarithm of a negative number (or zero) is not defined. SLO M-09-A-06 · Knowledge
72. log 0.01 =
- 2
- -3
- -2
- -1
Answer: C) -2
Explanation: 0.01 = 10^-2, so log 0.01 = -2. SLO M-09-A-07 · Knowledge
73. In the Babylonian base-60 system, a number written as 3 sixties and 5 ones equals:
- 305
- 35
- 185
- 175
Answer: C) 185
Explanation: Each place is worth 60 times the one to its right: 3 60 + 5 = 185. SLO M-09-A-01 · Knowledge
74. Which property is shown by if x = y then x + 13 = y + 13?
- Additive property of equality
- Additive property of inequality
- Additive inverse
- Additive identity
Answer: A) Additive property of equality
Explanation: if x = y then x + 13 = y + 13 is the additive property of equality. SLO M-09-A-03 · Knowledge
75. ln 1 =
- e
- undefined
- 1
- 0
Answer: D) 0
Explanation: e^0 = 1, so ln 1 = 0. SLO M-09-A-07 · Knowledge