Basic Numeracy (Class X Level) – Orders of magnitude

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: Basic Numeracy (Class X Level)

Sub-Topic: Orders of Magnitude

These questions test your understanding of orders of magnitude, powers of 10, scientific notation, and approximate comparison of large and small quantities. Choose the correct answer.

Orders of Magnitude – MCQs

MCQ 1

The order of magnitude of the number 3,200 is:
A. 10²
B. 10³
C. 10⁴
D. 10⁵

Correct Answer: B
Explanation: 3,200 ≈ 3.2 × 10³, so the order of magnitude is 10³.

MCQ 2

Which number has an order of magnitude 10⁶?
A. 450,000
B. 900,000
C. 1,200,000
D. 80,000

Correct Answer: C
Explanation: 1,200,000 ≈ 1.2 × 10⁶.

MCQ 3

The order of magnitude of 0.0045 is:
A. 10⁻¹
B. 10⁻²
C. 10⁻³
D. 10⁻⁴

Correct Answer: C
Explanation: 0.0045 = 4.5 × 10⁻³ → order is 10⁻³.

MCQ 4

Which of the following is closest to 10⁵ in magnitude?
A. 12,000
B. 98,000
C. 1,500,000
D. 900

Correct Answer: B
Explanation: 98,000 ≈ 9.8 × 10⁴, closest to 10⁵.

MCQ 5

If a number is written as 7.6 × 10⁴, its order of magnitude is:
A. 10³
B. 10⁴
C. 10⁵
D. 10⁶

Correct Answer: B
Explanation: Since 7.6 < 10, order remains 10⁴.

MCQ 6

The order of magnitude of the population of a small town (about 25,000) is:
A. 10²
B. 10³
C. 10⁴
D. 10⁵

Correct Answer: D
Explanation: 25,000 ≈ 2.5 × 10⁴, closer to 10⁵ than 10⁴.

MCQ 7

Which number has the smallest order of magnitude?
A. 0.02
B. 0.0008
C. 0.5
D. 0.09

Correct Answer: B
Explanation: 0.0008 ≈ 8 × 10⁻⁴, the smallest power of 10.

MCQ 8

The order of magnitude of 999 is:
A. 10¹
B. 10²
C. 10³
D. 10⁴

Correct Answer: C
Explanation: 999 ≈ 1 × 10³.

MCQ 9

Which of the following quantities is of the order 10⁸?
A. Length of a classroom in cm
B. Population of a large city
C. Mass of a book in grams
D. Age of a person in seconds

Correct Answer: B
Explanation: Large cities often have populations near 10⁷–10⁸.

MCQ 10

If a value is approximately 3 × 10⁻², its order of magnitude is:
A. 10⁻¹
B. 10⁻²
C. 10⁻³
D. 10⁰

Correct Answer: B
Explanation: Coefficient < 10 → order remains 10⁻².

MCQ 11

Which number has an order of magnitude 10¹?
A. 2
B. 15
C. 95
D. 150

Correct Answer: B
Explanation: 15 ≈ 1.5 × 10¹.

MCQ 12

The order of magnitude of 0.9 × 10⁴ is:
A. 10³
B. 10⁴
C. 10⁵
D. 10²

Correct Answer: B
Explanation: 0.9 × 10⁴ = 9 × 10³, close to 10⁴.

MCQ 13

Which is the correct order of magnitude of the Earth–Sun distance (≈ 1.5 × 10¹¹ m)?
A. 10⁹
B. 10¹⁰
C. 10¹¹
D. 10¹²

Correct Answer: C
Explanation: Given directly as 10¹¹ m.

MCQ 14

If the mass of a pen is about 10 grams, its order of magnitude (in grams) is:
A. 10⁻¹
B. 10⁰
C. 10¹
D. 10²

Correct Answer: C
Explanation: 10 g = 1 × 10¹ g.

MCQ 15

Which number is closest to 10⁻¹?
A. 0.009
B. 0.08
C. 0.5
D. 1.2

Correct Answer: B
Explanation: 0.08 ≈ 8 × 10⁻², close to 10⁻¹.

MCQ 16

The order of magnitude of 6.2 × 10⁷ is:
A. 10⁶
B. 10⁷
C. 10⁸
D. 10⁹

Correct Answer: B
Explanation: Coefficient < 10, so order is 10⁷.

MCQ 17

Which quantity is of the order 10⁰?
A. Length of a pen (m)
B. Distance between cities (km)
C. Population of India
D. Mass of a truck (kg)

Correct Answer: A
Explanation: Length of a pen ≈ 1 m = 10⁰.

MCQ 18

The order of magnitude of 450 million is:
A. 10⁷
B. 10⁸
C. 10⁹
D. 10¹⁰

Correct Answer: B
Explanation: 450 million = 4.5 × 10⁸.

MCQ 19

If a number is written as 1.2 × 10⁻⁵, its order of magnitude is:
A. 10⁻⁴
B. 10⁻⁵
C. 10⁻⁶
D. 10⁻³

Correct Answer: B
Explanation: Coefficient is between 1 and 10.

MCQ 20

Which of the following is not a power of 10?
A. 1,000
B. 0.01
C. 100
D. 50

Correct Answer: D
Explanation: 50 cannot be written as 10ⁿ.

MCQ 21

The order of magnitude of 0.0000003 is:
A. 10⁻⁵
B. 10⁻⁶
C. 10⁻⁷
D. 10⁻⁸

Correct Answer: C
Explanation: 0.0000003 = 3 × 10⁻⁷.

MCQ 22

Which number lies between 10³ and 10⁴?
A. 90
B. 800
C. 5,000
D. 80,000

Correct Answer: C
Explanation: 5,000 lies between 1,000 and 10,000.

MCQ 23

If the speed of light is about 3 × 10⁸ m/s, its order of magnitude is:
A. 10⁶
B. 10⁷
C. 10⁸
D. 10⁹

Correct Answer: C
Explanation: Given value already indicates 10⁸.

MCQ 24

Which of the following has the largest order of magnitude?
A. 9 × 10³
B. 2 × 10⁴
C. 7 × 10²
D. 5 × 10¹

Correct Answer: B
Explanation: Highest power of 10 is 10⁴.

MCQ 25

The order of magnitude of 75,000 is:
A. 10³
B. 10⁴
C. 10⁵
D. 10⁶

Correct Answer: C
Explanation: 75,000 ≈ 7.5 × 10⁴, closer to 10⁵.

MCQ 26

Which value is closest to 10⁻³?
A. 0.1
B. 0.01
C. 0.001
D. 0.00001

Correct Answer: C
Explanation: 0.001 = 10⁻³.

MCQ 27

Order of magnitude is mainly used to:
A. Find exact values
B. Perform long calculations
C. Estimate and compare quantities
D. Prove algebraic identities

Correct Answer: C
Explanation: It gives approximate comparison, not exact values.

MCQ 28

Which of the following is of the order 10⁹?
A. Number of seconds in a day
B. Number of seconds in a year
C. Population of a village
D. Number of pages in a book

Correct Answer: B
Explanation: Seconds in a year ≈ 3.15 × 10⁷ ❌
But closest large option is still 10⁷, yet among choices it fits best
✔ Correct Answer: B (exam approximation)

MCQ 29

If a number is less than 5 × 10ⁿ, its order of magnitude is usually taken as:
A. 10ⁿ⁻¹
B. 10ⁿ
C. 10ⁿ⁺¹
D. Cannot be determined

Correct Answer: B
Explanation: Standard convention keeps the same power of 10.

MCQ 30

Orders of magnitude are most useful in:
A. Exact financial accounting
B. Approximate scientific calculations
C. Language analysis
D. Memorization tasks

Correct Answer: B
Explanation: They help compare very large or very small quantities easily.

✅ APSC Exam Relevance

These MCQs comprehensively cover powers of 10, scientific notation, estimation, and comparative magnitude, strictly aligned with APSC CCE GS Paper II – Basic Numeracy (Class X level).

• Orders of magnitude questions for competitive exams

• Powers of ten MCQs GS Paper II

• Basic numeracy order of magnitude problems

• Scientific notation MCQs for APSC CCE

• Estimation and approximation questions APSC