126. Which fraction has a terminating decimal expansion?
- 57
- 112
- 320
- 49
Answer: C) 320
Explanation: A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5. 320 = 0.15. SLO M-09-A-02 · Knowledge
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 6)
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.
127. A shirt marked at Rs. 3,600 is sold at a 12.5% discount. The sale price is:
- Rs. 3,587
- Rs. 450
- Rs. 3,150
- Rs. 4,050
Answer: C) Rs. 3,150
Explanation: Discount = 12.5% of 3600 = 450. Sale price = 3600 - 450 = 3150. SLO M-09-A-09 · Application
128. Write [3]250 in simplest form.
- 5 [3]2
- 2 [3]5
- 6 [3]2
- 5 2
Answer: A) 5 [3]2
Explanation: 250 = 125 2, so [3]250 = 5 [3]2. SLO M-09-A-04 · Application
129. The word algorithm comes from the name of the Muslim mathematician:
- Al-Biruni
- Al-Khwarizmi
- Omar Khayyam
- Ibn Sina
Answer: B) Al-Khwarizmi
Explanation: Muhammad ibn Musa al-Khwarizmi (9th century, Baghdad) wrote on Hindu numerals; the Latin form of his name, Algoritmi, gave us the word algorithm. SLO M-09-A-01 · Knowledge
130. If a b and c 0, then:
- ac = bc
- ac < bc
- ac bc
- a - c < b - c
Answer: C) ac bc
Explanation: Multiplying both sides of an inequality by a positive number keeps the sign the same. SLO M-09-A-03 · Knowledge
131. Which of the following is an irrational number?
- 0.overline3
- 0.09
- 1+ 3
- 49
Answer: C) 1+ 3
Explanation: 1+ 3 is irrational because a rational number plus an irrational number is irrational. The others can be written as pq (e.g. 49 = 7, 0.overline3 = 13). SLO M-09-A-02 · Knowledge
132. Which property is shown by 12 + 14 = 14 + 12?
- Commutative property of addition
- Associative property of multiplication
- Associative property of addition
- Commutative property of multiplication
Answer: A) Commutative property of addition
Explanation: 12 + 14 = 14 + 12 is the commutative property of addition. SLO M-09-A-03 · Knowledge
133. Write 9.1 10^5 as an ordinary number.
- 910,000
- 91,000
- 9,100,000
- 0.000091
Answer: A) 910,000
Explanation: Move the decimal point 5 places to the right: 910,000. SLO M-09-A-05 · Understanding
134. Which of the following is a rational number?
- 2
- 144
- 1+ 3
- pi
Answer: B) 144
Explanation: 144 can be written as pq with q neq 0, so it is rational. The others are irrational. SLO M-09-A-02 · Knowledge
135. Write 0.00208 in scientific notation.
- 2.08 10^-3
- 2.08 10^3
- 2.08 10^-4
- 2.08 10^-2
Answer: A) 2.08 10^-3
Explanation: Move the decimal point so that one non-zero digit is before it: 0.00208 = 2.08 10^-3 (right by 3 places). SLO M-09-A-05 · Understanding
136. The characteristic of log 4567 is:
- 3
- 5
- 1
- bar1
Answer: A) 3
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
137. The discovery that 2 cannot be written as a fraction is credited to:
- Fibonacci
- the Romans
- the Babylonians
- the Pythagoreans (Hippasus)
Answer: D) the Pythagoreans (Hippasus)
Explanation: Members of the Pythagorean school in ancient Greece (traditionally Hippasus) found that the diagonal of a unit square, 2, is irrational. SLO M-09-A-01 · Knowledge
138. If logx 64 = 6, then x =
- 1
- 12
- 2
- 3
Answer: C) 2
Explanation: x^6 = 64, so x = [6]64 = 2. SLO M-09-A-06 · Knowledge
139. How many different digits are needed to write any whole number in the Hindu–Arabic (decimal) system?
- 60
- Unlimited
- 10
- 9
Answer: C) 10
Explanation: The ten digits 0, 1, 2, ldots, 9 with place value are enough for any whole number. SLO M-09-A-01 · Knowledge
140. Find log2 ( 18 ).
- 3
- -3
- -2
- -6
Answer: B) -3
Explanation: log2 x = y means 2^y = x. Since 2^-3 = 18, the answer is -3. SLO M-09-A-06 · Knowledge
141. A family earns Rs. 60,000 a month. It spends 25 on rent and 14 on food. How much is left?
- Rs. 21,000
- Rs. 15,000
- Rs. 54,000
- Rs. 24,000
Answer: A) Rs. 21,000
Explanation: Fraction left = 1 - 25 - 14 = 720, and 720 60000 = 21000. SLO M-09-A-09 · Application
142. Expand log ( a, b^3 ).
- 2log a + 3log b
- 12log a + 3log b
- 12log a 3log b
- log a2 + log 3b
Answer: B) 12log a + 3log b
Explanation: a = a^1/2, so the logs are 12log a + 3log b. SLO M-09-A-08 · Application
143. Money grows by 5% per year (compound): A = A0(1.05)^t. About how many years until it becomes 3 times as much? (use logarithms)
- 22.5 years
- 20.5 years
- 40.0 years
- 24.5 years
Answer: A) 22.5 years
Explanation: (1.05)^t = 3 Rightarrow t = log 3log 1.05 approx 22.5 years. SLO M-09-A-08 · Application
144. Which property is shown by 2 + 0 = 2?
- Additive inverse
- Additive property of equality
- Additive property of inequality
- Additive identity
Answer: D) Additive identity
Explanation: 2 + 0 = 2 is the additive identity. SLO M-09-A-03 · Knowledge
145. Write 7,050,000,000 in scientific notation.
- 7.05 10^8
- 7.05 10^10
- 7.05 10^9
- 7.05 10^-9
Answer: C) 7.05 10^9
Explanation: Move the decimal point so that one non-zero digit is before it: 7,050,000,000 = 7.05 10^9 (left by 9 places). SLO M-09-A-05 · Understanding
146. Write 0.1overline6 as a fraction in lowest terms.
- 1699
- 845
- 425
- 16
Answer: D) 16
Explanation: Let x = 0.1overline6. Then 100x - 10x = 16 - 1 = 15, so x = 1590 = 16. SLO M-09-A-02 · Knowledge
147. Which of the following is an irrational number?
- -38
- [3]5
- 227
- 0.09
Answer: B) [3]5
Explanation: [3]5 is irrational because 5 is not a perfect cube. The others can be written as pq (e.g. 49 = 7, 0.overline3 = 13). SLO M-09-A-02 · Knowledge
148. Simplify 2 2 + 3 18.
- 5 4
- 11 2
- 12 2
- 5 18
Answer: B) 11 2
Explanation: 18 = 3 2, so the sum is 2 2 + 9 2 = 11 2. SLO M-09-A-04 · Application
149. log 100000 =
- 4
- 6
- -5
- 5
Answer: D) 5
Explanation: 100000 = 10^5, so log 100000 = 5. SLO M-09-A-07 · Knowledge
150. Sound level is L = 10 log ( II0 ) decibels. A sound 1,000 times as intense as I0 has a level of:
- 30 dB
- 100 dB
- 40 dB
- 3 dB
Answer: A) 30 dB
Explanation: L = 10 log 10^3 = 10 3 = 30 dB. SLO M-09-A-08 · Application