ACT Math Scientific Notation: 17 Practice Problems with Step-by-Step Explanations
Scientific notation writes very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of 10, like 1.7 × 106. The ACT tests both basic conversion (turning a normal number into scientific notation and back) and arithmetic performed directly on numbers already in scientific notation — addition, subtraction, multiplication, and division — each of which follows its own specific rule.
Multiplying and dividing are the most mechanical: multiply (or divide) the coefficients together, and add (or subtract) the exponents. Addition and subtraction are trickier, since you can only combine the coefficients directly when both numbers share the exact same power of 10 — if they don't, rewrite one number so the powers match before adding or subtracting. After any operation, check whether the resulting coefficient is still between 1 and 10; if it isn't (like 26.25 or 0.419), shift the decimal point and adjust the exponent to bring it back into proper scientific notation form.
Common traps include forgetting to renormalize the coefficient after an operation (leaving an answer like 33.8 × 105 instead of converting it to 3.38 × 106), mismatching exponents before adding or subtracting, and on percentage or ratio problems involving scientific notation, doing the percentage or division calculation before converting units consistently. Work through the 17 problems below, then click to reveal each step-by-step explanation.
On this page:
- Problem 1 — Converting to scientific notation
- Problem 2 — Subtraction, then scientific notation
- Problem 3 — Adding in scientific notation
- Problem 4 — Subtracting in scientific notation
- Problem 5 — Dividing in scientific notation
- Problem 6 — Multiplying in scientific notation
- Problem 7 — Rate and time conversion
- Problem 8 — Percentage of a value
- Problem 9 — Ratio of two values
- Problem 10 — Evaluating an expression
- Problem 11 — Finding an exponent
- Problem 12 — Probability with scientific notation
- Problem 13 — Dividing by a constant
- Problem 14 — Solving for a variable exponent
- Problem 15 — Converting a decimal coefficient
- Problem 16 — Percentage in scientific notation
- Problem 17 — Rewriting with a negative exponent
Practice Problems
A portion of the Great Wall of China has approximately 1.7 million stone blocks. Which of the following expressions, when written in scientific notation, is equivalent to the number of blocks used to construct the portion of the Great Wall of China?
- A) 1.7×104
- B) 1.7×105
- C) 1.7×106
- D) 17×105
1.7 million = 1,700,000. In scientific notation, this is written with a coefficient between 1 and 10: 1.7×106.
A beachfront condo was purchased in 1995 for $210,000. If the condo was sold in 2022 for $1,450,000, which of the following expressions represents the increase in the value of the condo from 1995 to 2022?
- A) 1.24×105
- B) 1.24×106
- C) 1.45×106
- D) 1.66×106
Subtract the original price from the sale price: 1,450,000 − 210,000 = 1,240,000.
In scientific notation: 1.24×106.
Which of the following expressions represents the sum of 2.6×106 and 7.8×105 in scientific notation?
- A) 2.03×1011
- B) 3.38×106
- C) 8.06×105
- D) 8.06×106
Rewrite both numbers with matching powers of 10: 2.6×106 = 26×105.
Add: 26×105 + 7.8×105 = 33.8×105. Renormalize the coefficient: 33.8×105 = 3.38×106.
Which of the following expressions represents the difference of 9.7×107 and 4.3×106 in scientific notation?
- A) 5.4×106
- B) 5.4×107
- C) 9.27×106
- D) 9.27×107
Rewrite both numbers with matching powers of 10: 9.7×107 = 97×106.
Subtract: 97×106 − 4.3×106 = 92.7×106. Renormalize: 92.7×106 = 9.27×107.
(7.5×10−3) / (1.5×10−5) = ?
- A) 5×102
- B) 5×10−2
- C) 5×10−8
- D) 6×102
Divide the coefficients: 7.5/1.5 = 5. Subtract the exponents: −3−(−5) = 2.
Result: 5×102.
(21.4×104)(4×106) = ?
- A) 2.54×1010
- B) 8.56×1010
- C) 2.54×1011
- D) 8.56×1011
Multiply the coefficients: 21.4×4 = 85.6. Add the exponents: 4+6=10.
Result: 85.6×1010. Renormalize: 85.6×1010 = 8.56×1011.
Jordan's average heart rate is 65 beats per minute. In scientific notation, how many times would Jordan's heart beat in 24 hours?
- A) 1.56×103
- B) 3.90×103
- C) 9.36×103
- D) 9.36×104
Convert 24 hours to minutes: 24×60 = 1,440 minutes.
Total beats: 65×1,440 = 93,600. In scientific notation: 9.36×104.
What is 8% of 9.02×104?
- A) 7,216
- B) 11,275
- C) 72,160
- D) 112,750
9.02×104 = 90,200. Multiply by 0.08: 90,200×0.08 = 7,216.
The area of Connecticut is 1.44×104 square kilometers. The area of Canada is 9.89×106 square kilometers. Using these measurements, which of the following is closest to the ratio of the area of Canada to Connecticut?
- A) 48:5
- B) 98:14
- C) 144:989
- D) 687:1
Divide Canada's area by Connecticut's area: (9.89×106)/(1.44×104) = (9.89/1.44)×102 ≈ 6.868×100 ≈ 686.8.
This rounds to a ratio of about 687:1.
The value of x6(0.2x2+2.2x+7) is between which of the following numbers when x=10?
- A) 4×106 and 5×106
- B) 4×107 and 5×107
- C) 4×108 and 5×108
- D) 1×108 and 1×109
At x=10: x6=106=1,000,000. Inside the parentheses: 0.2(100)+2.2(10)+7 = 20+22+7 = 49.
Total: 1,000,000×49 = 49,000,000 = 4.9×107, which falls between 4×107 and 5×107.
A truck can carry 12,480 oranges. If the number of oranges carried by 2,500 trucks can be expressed as 3.12×10n, what is the value of n?
- A) 5
- B) 6
- C) 7
- D) 8
Total oranges: 12,480×2,500 = 31,200,000.
In scientific notation: 3.12×107, so n=7.
About 9.5×104 square miles of Alaska is water. The rest of Alaska, about 5.7×105 square miles, is land. If a point in Alaska is randomly selected, what is the probability the selected point is in water?
- A) 14.3%
- B) 16.7%
- C) 27.5%
- D) 60.0%
Total area: 9.5×104 + 5.7×105 = 0.95×105 + 5.7×105 = 6.65×105.
Probability of water: (9.5×104)/(6.65×105) = 0.95/6.65 ≈ 0.1429 ≈ 14.3%.
The circumference of the Earth is approximately 131.4 million feet. Which of the following expressions is closest to the radius of the Earth, in feet, when expressed in scientific notation?
- A) 6.47×103
- B) 2.09×107
- C) 4.18×107
- D) 2.09×108
131.4 million = 1.314×108 feet. Radius = circumference/(2π): 1.314×108/(2π) ≈ 1.314×108/6.2832.
≈ 2.09×107 feet.
What value of a makes the equation below true?
(3.75×103a+6)(7×1012) = 26,250
- A) −6
- B) −5
- C) −4
- D) −3
Multiply the coefficients: 3.75×7 = 26.25. Add the exponents: (3a+6)+12 = 3a+18. So the left side becomes 26.25×103a+18.
Rewrite 26,250 in scientific notation: 2.625×104. Since 26.25 = 2.625×10, the equation becomes 2.625×103a+19 = 2.625×104, so 3a+19=4, giving 3a=−15 and a=−5.
If x = 0.00419×10c and c is an integer, what is the scientific notation for x?
- A) 4.19×10c−3
- B) 4.19×10c−2
- C) 4.19×10c+2
- D) 4.19×10c+3
First convert 0.00419 to scientific notation: 0.00419 = 4.19×10−3.
Substitute: x = 4.19×10−3×10c = 4.19×10c−3.
A 0.005g sample of an unknown metal is analyzed and is found to be 0.03% silver. Which of the following expressions correctly expresses the mass of silver, in grams, in scientific notation?
- A) 1.5×10−3
- B) 1.5×10−4
- C) 1.5×10−5
- D) 1.5×10−6
Convert 0.03% to a decimal: 0.0003. Multiply by the sample mass: 0.005×0.0003 = 0.0000015.
In scientific notation: 1.5×10−6.
If z < 0, which of the following expressions is equivalent to (70,000)z?
- A) (7)−z×104
- B) (7)z×10−4z
- C) (1/7)z×104z
- D) (1/7)−z×104z
Rewrite 70,000 as 7×104, so (70,000)z = (7×104)z = 7z×104z.
Since (1/7)−z = 7z, option D — (1/7)−z×104z — is equivalent to 7z×104z, matching exactly.
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