Powers of 10 & Scientific Notation — Practice Set

Bank code: ARI-P10 · Section: Arithmetic · 30 questions — Easy 5 · Medium 8 · Hard 12 · Extreme 5

Separate the digits from the size: compare exponents first, and renormalise so the coefficient sits between 1 and 10.

Every question below is live in the question bank under the ID shown — the sheet and the portal are the same questions. Attempt a level with the clock running, then check Part C.

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Part A — Questions

Quantitative Comparison — the four choices are always the same, so they are not reprinted: (A) Column A is greater · (B) Column B is greater · (C) The two quantities are equal · (D) The relationship cannot be determined from the information given

Level 1 · Easy — 5 questions · ~4 min

warm-up — these must be automatic

Q1 · ARI-P10-003 · MCQ · 40s

What is the value of 10^(-2)?

(A) -100
(B) -0.01
(C) 0.001
(D) 0.01
(E) 0.1

Q2 · ARI-P10-004 · Numeric Entry · 50s

The number 0.00056 is written in scientific notation as a x 10^n, where 1 <= a < 10. What is the value of n? Enter your answer as a number.

Numeric entry — write the number.

Q3 · ARI-P10-005 · MCQ · 45s

Which of the following expresses 45,000 in correct scientific notation?

(A) 45 x 10^3
(B) 4.5 x 10^3
(C) 4.5 x 10^4
(D) 0.45 x 10^5
(E) 4.5 x 10^5

Q4 · ARI-P10-009 · MCQ · 40s

The population of a city is approximately 2.4 x 10^6. Which of the following is this population written out in full?

(A) 240,000
(B) 2,400,000
(C) 24,000,000
(D) 240,000,000
(E) 0.0000024

Q5 · ARI-P10-010 · Select all that apply · 60s

Which of the following are equal to 0.001? Select all that apply.

(A) 10^(-3)
(B) 1/10^3
(C) 10^(-1) x 10^(-2)
(D) 10^(-1) + 10^(-2)
(E) 1/10^(-3)

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · ARI-P10-012 · MCQ · 70s

What is (5 x 10^3)(4 x 10^6) expressed in correct scientific notation?

(A) 9 x 10^9
(B) 2 x 10^9
(C) 2 x 10^10
(D) 20 x 10^9
(E) 20 x 10^18

Q7 · ARI-P10-013 · Numeric Entry · 65s

If 4.8 x 10^n = 480,000, what is the value of n? Enter your answer as a number.

Numeric entry — write the number.

Q8 · ARI-P10-014 · QC · 65s

Column A: (2 x 10^3)^2 Column B: 4 x 10^6

Q9 · ARI-P10-016 · QC · 65s

Column A: 10^(-3) Column B: (0.1)^3

Q10 · ARI-P10-019 · Select all that apply · 75s

Which of the following numbers have a NEGATIVE exponent when written in scientific notation? Select all that apply.

(A) 0.0083
(B) 8,300
(C) 0.83
(D) 1
(E) 0.00083

Q11 · ARI-P10-021 · MCQ · 85s

Let X = 0.72 x 10^(-3), Y = 9.1 x 10^(-4), and Z = 830 x 10^(-6). Which of the following orders these three numbers from least to greatest?

(A) X < Y < Z
(B) X < Z < Y
(C) Z < X < Y
(D) Z < Y < X
(E) Y < Z < X

Q12 · ARI-P10-022 · Numeric Entry · 85s

The distance from Earth to the Sun is approximately 1.5 x 10^8 km, and the distance from Earth to the Moon is approximately 3.8 x 10^5 km. Approximately how many times as far from Earth is the Sun as the Moon? Round to the nearest whole number and enter your answer as a number.

Numeric entry — write the number.

Q13 · ARI-P10-025 · Select all that apply · 80s

Which of the following expressions are equal to 10^6? Select all that apply.

(A) (10^2)^3
(B) 10^12 / 10^2
(C) 10^8 x 10^(-2)
(D) 10^3 + 10^3
(E) (10^(-2))^(-3)

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Level 3 · Hard — 12 questions · ~19 min

where 162+ is won or lost

Q14 · ARI-P10-027 · MCQ · 95s

Given that 2^10 is approximately 10^3, approximately how many digits does 2^40 have?

(A) 4
(B) 12
(C) 13
(D) 41
(E) 121

Q15 · ARI-P10-028 · Numeric Entry · 95s

If 10^x = 5 x 10^7 and 10^y = 2 x 10^3, what is the value of x + y? Enter your answer as a number.

Numeric entry — write the number.

Q16 · ARI-P10-029 · QC · 85s

Column A: (3 x 10^(-4)) - (2 x 10^(-5)) Column B: 2.8 x 10^(-4)

Q17 · ARI-P10-030 · MCQ · 100s

The mass of a proton is approximately 1.67 x 10^(-27) kg and the mass of an electron is approximately 9.11 x 10^(-31) kg. Approximately how many times as heavy as an electron is a proton?

(A) 1.83 x 10^(-58)
(B) 5.5 x 10^(-4)
(C) 1.83 x 10^3
(D) 1.83 x 10^4
(E) 1.83 x 10^5

Q18 · ARI-P10-031 · Numeric Entry · 90s

The quotient (2.4 x 10^8) / (8 x 10^(-4)) is written in scientific notation as a x 10^n, where 1 <= a < 10. What is the value of n? Enter your answer as a number.

Numeric entry — write the number.

Q19 · ARI-P10-032 · Select all that apply · 100s

For which of the following values of n is (2 x 10^n)(5 x 10^(-4)) < 10^(-6)? Select all that apply.

(A) n = -6
(B) n = -5
(C) n = -4
(D) n = -3
(E) n = -2

Q20 · ARI-P10-033 · QC · 90s

n is a positive integer.

Column A: 9 x 10^n + 10^n Column B: 10^(n+1)

Q21 · ARI-P10-034 · MCQ · 100s

In 2020 Country A had a GDP of 2.1 x 10^13 dollars and Country B had a GDP of 1.4 x 10^12 dollars. Country A's GDP was approximately what percent GREATER than Country B's GDP?

(A) 15%
(B) 93%
(C) 150%
(D) 1,400%
(E) 1,500%

Q22 · ARI-P10-035 · Numeric Entry · 95s

If 10^a = 64 and 10^b = 0.25, what is the value of 10^(a + 2b)? Enter your answer as a number.

Numeric entry — write the number.

Q23 · ARI-P10-036 · QC · 95s

Column A: The number of zeros between the decimal point and the first nonzero digit when (2 x 10^(-4))(5 x 10^(-3)) is written as a decimal Column B: 6

Q24 · ARI-P10-041 · MCQ · 105s

Which of the following is closest in value to (4.1 x 10^7)(5.9 x 10^(-3)) / (1.9 x 10^(-4))?

(A) 1.3 x 10^1
(B) 1.3 x 10^8
(C) 1.3 x 10^9
(D) 2.4 x 10^9
(E) 1.3 x 10^15

Q25 · ARI-P10-042 · MCQ · 105s

A certain virus has diameter 3 x 10^(-8) meters and a certain bacterium has diameter 1.2 x 10^(-6) meters. Both are modelled as spheres, and the volume of a sphere is proportional to the cube of its diameter. Approximately how many times as large as the volume of the virus is the volume of the bacterium?

(A) 1.6 x 10^(-5)
(B) 2.5 x 10^(-2)
(C) 4 x 10^1
(D) 4 x 10^3
(E) 6.4 x 10^4

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Level 4 · Extreme — 5 questions · ~10 min

165+ — expect to need the insight, not the grind

Q26 · ARI-P10-037 · MCQ · 120s

If N = (10^24 - 1)/(10^8 - 1), which of the following is equal to N?

(A) 10^3
(B) 10^16
(C) 10^16 + 1
(D) 10^16 - 10^8 + 1
(E) 10^16 + 10^8 + 1

Q27 · ARI-P10-038 · Numeric Entry · 115s

The number 10^100 is called a googol. When 1/(4 x 10^100) is written as a decimal, how many zeros lie between the decimal point and the first nonzero digit? Enter your answer as a number.

Numeric entry — write the number.

Q28 · ARI-P10-039 · QC · 125s

p and q are nonnegative integers with p > q.

Column A: 10^p - 10^q Column B: 10^(p - q)

Q29 · ARI-P10-040 · Select all that apply · 125s

Let S = 10^1 + 10^2 + 10^3 + ... + 10^9. Which of the following are true? Select all that apply.

(A) S < 10^10
(B) S > 1.2 x 10^9
(C) S has exactly 10 digits
(D) The sum of the digits of S equals 9
(E) S = (10^9 - 10)/9

Q30 · ARI-P10-043 · MCQ · 125s

For how many integer values of n is (2.5 x 10^(-4))(4 x 10^(-3)) < 10^n < (5 x 10^6)^2?

(A) 14
(B) 18
(C) 19
(D) 20
(E) 21

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