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Exponents and Scientific Notation Practice Tests

These Grade 8 Math practice tests cover exponent rules, zero and negative exponents, powers of 10, scientific notation, operations, comparisons, and real-world measurements.

Skills covered

  • Evaluating powers and applying product, quotient, power-of-a-power, and power-of-a-product rules
  • Interpreting zero and negative exponents and writing reciprocal forms
  • Converting between standard form and scientific notation
  • Multiplying, dividing, adding, and comparing numbers in scientific notation
  • Using powers of 10 to describe very large and very small measurements

How to use these practice tests

Identify the base and exponent first. For scientific notation, count decimal places and confirm that the coefficient is at least 1 and less than 10. Keep units when solving real-world problems.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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5. Test

Grade 8 Exponents and Scientific Notation Practice Tests

Practice Grade 8 Math questions about exponent rules, powers of ten, negative exponents, scientific notation, operations, comparisons, and real-world scale.

Choose the best answer for each question. Write powers and scientific notation carefully, then review the explanation after submitting your answers.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

The mass of a grain of sand is about 2.5×10−62.5\times10^{-6} grams. What does the negative exponent show?

Please select an answer first.

Correct answer: A

The correct answer is The mass is much smaller than 1 gram..

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: A negative power of 10 places the decimal to the left, so the positive mass is a small fraction of a gram.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

A negative power of 10 places the decimal to the left, so the positive mass is a small fraction of a gram.

2. QuestionMultiple choice

The distance from a planet to a star is 1.2×1081.2\times10^8 kilometers. What is its standard form?

Please select an answer first.

Correct answer: B

The correct answer is 120,000,000120,000,000 kilometers.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Move the decimal eight places right: 1.2×108=120,000,0001.2\times10^8=120,000,000.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Move the decimal eight places right: 1.2×108=120,000,0001.2\times10^8=120,000,000.

3. QuestionMultiple choice

A file has size 6×1066\times10^6 bytes and another has size 2×1062\times10^6 bytes. What is their total size?

Please select an answer first.

Correct answer: C

The correct answer is 8×1068\times10^6 bytes.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Because the powers match, add the coefficients: (6+2)×106=8×106(6+2)\times10^6=8\times10^6.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Because the powers match, add the coefficients: (6+2)×106=8×106(6+2)\times10^6=8\times10^6.

4. QuestionMultiple choice

A microscope image is 4×10−34\times10^{-3} meters wide. Which decimal represents this width?

Please select an answer first.

Correct answer: D

The correct answer is 0.0040.004 meters.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Move the decimal three places left: 4×10−3=0.0044\times10^{-3}=0.004.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Move the decimal three places left: 4×10−3=0.0044\times10^{-3}=0.004.

5. QuestionMultiple choice

Which measurement is greatest?

Please select an answer first.

Correct answer: A

The correct answer is 3.5×1073.5\times10^7.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: The exponent 7 is greater than 6, 5, and 4, so 3.5×1073.5\times10^7 has the greatest magnitude.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

The exponent 7 is greater than 6, 5, and 4, so 3.5×1073.5\times10^7 has the greatest magnitude.

6. QuestionMultiple choice

Why is scientific notation useful for very large or very small measurements?

Please select an answer first.

Correct answer: B

The correct answer is It shows the significant scale with fewer zeros and makes comparisons and calculations easier..

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Scientific notation preserves the value while making place value and powers of 10 explicit.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Scientific notation preserves the value while making place value and powers of 10 explicit.

7. QuestionMultiple choice

Which is the best estimate for (4.8×103)+(2.1×103)(4.8\times10^3)+(2.1\times10^3)?

Please select an answer first.

Correct answer: C

The correct answer is 7×1037\times10^3.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: The exact sum is 6.9×1036.9\times10^3, which is closest to 7×1037\times10^3.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

The exact sum is 6.9×1036.9\times10^3, which is closest to 7×1037\times10^3.

8. QuestionMultiple choice

Which statement correctly compares 2.4×10−32.4\times10^{-3} and 2.4×10−52.4\times10^{-5}?

Please select an answer first.

Correct answer: D

The correct answer is 2.4×10−3>2.4×10−52.4\times10^{-3}>2.4\times10^{-5}.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: With the same positive coefficient, 10−310^{-3} is 100 times greater than 10−510^{-5}.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

With the same positive coefficient, 10−310^{-3} is 100 times greater than 10−510^{-5}.

9. QuestionMultiple choice

A calculator displays 6.02×10236.02\times10^{23}. Which statement is correct?

Please select an answer first.

Correct answer: A

The correct answer is The value is approximately 602,000,000,000,000,000,000,000..

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Move the decimal 23 places right to interpret the positive exponent; the displayed scientific notation represents a very large number.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Move the decimal 23 places right to interpret the positive exponent; the displayed scientific notation represents a very large number.

10. QuestionMultiple choice

What is the main reason to keep units when using scientific notation?

Please select an answer first.

Correct answer: B

The correct answer is Units identify what the measured number represents and help prevent incorrect comparisons or conversions..

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: A numerical value without its unit can be misunderstood, especially when comparing mass, distance, time, or data size.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

A numerical value without its unit can be misunderstood, especially when comparing mass, distance, time, or data size.

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