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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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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

Which is the scientific notation for 4,500,0004,500,000?

Please select an answer first.

Correct answer: A

The correct answer is 4.5×1064.5\times10^6.

  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 six places left to get a coefficient from 1 through 10: 4,500,000=4.5×1064,500,000=4.5\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.

Move the decimal six places left to get a coefficient from 1 through 10: 4,500,000=4.5×1064,500,000=4.5\times10^6.

2. QuestionMultiple choice

Which is the scientific notation for 0.000720.00072?

Please select an answer first.

Correct answer: B

The correct answer is 7.2×10−47.2\times10^{-4}.

  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 four places right to get 7.2, so the exponent is -4: 0.00072=7.2×10−40.00072=7.2\times10^{-4}.
  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 four places right to get 7.2, so the exponent is -4: 0.00072=7.2×10−40.00072=7.2\times10^{-4}.

3. QuestionMultiple choice

Which number is equal to 3.6×1053.6\times10^5?

Please select an answer first.

Correct answer: C

The correct answer is 360,000360,000.

  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: A positive exponent moves the decimal five places right: 3.6×105=360,0003.6\times10^5=360,000.
  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.

A positive exponent moves the decimal five places right: 3.6×105=360,0003.6\times10^5=360,000.

4. QuestionMultiple choice

Which number is equal to 8.1×10−38.1\times10^{-3}?

Please select an answer first.

Correct answer: D

The correct answer is 0.00810.0081.

  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 exponent moves the decimal three places left: 8.1×10−3=0.00818.1\times10^{-3}=0.0081.
  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 exponent moves the decimal three places left: 8.1×10−3=0.00818.1\times10^{-3}=0.0081.

5. QuestionMultiple choice

Which number is greater?

Please select an answer first.

Correct answer: A

The correct answer is 6.2×1046.2\times10^4.

  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: Both first values have the same coefficient comparison, and 104>10310^4>10^3, so 6.2×1046.2\times10^4 is greater than the alternatives.
  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.

Both first values have the same coefficient comparison, and 104>10310^4>10^3, so 6.2×1046.2\times10^4 is greater than the alternatives.

6. QuestionMultiple choice

What is the standard form of 9.03×1029.03\times10^2?

Please select an answer first.

Correct answer: B

The correct answer is 903903.

  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 two places right: 9.03×102=9039.03\times10^2=903.
  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 two places right: 9.03×102=9039.03\times10^2=903.

7. QuestionMultiple choice

What is the standard form of 1.45×10−51.45\times10^{-5}?

Please select an answer first.

Correct answer: C

The correct answer is 0.00001450.0000145.

  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 five places left: 1.45×10−5=0.00001451.45\times10^{-5}=0.0000145.
  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 five places left: 1.45×10−5=0.00001451.45\times10^{-5}=0.0000145.

8. QuestionMultiple choice

Which coefficient is valid in scientific notation?

Please select an answer first.

Correct answer: D

The correct answer is 7.47.4.

  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 uses a coefficient at least 1 and less than 10, so 7.4 is valid.
  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 uses a coefficient at least 1 and less than 10, so 7.4 is valid.

9. QuestionMultiple choice

What does a negative exponent of 10 usually indicate in scientific notation?

Please select an answer first.

Correct answer: A

The correct answer is A number smaller than 1.

  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 exponent moves the decimal left and represents a positive value smaller than 1 when the coefficient is positive.
  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 exponent moves the decimal left and represents a positive value smaller than 1 when the coefficient is positive.

10. QuestionMultiple choice

Why is 32×10432\times10^4 not written in standard scientific notation?

Please select an answer first.

Correct answer: B

The correct answer is Its coefficient is not between 1 and 10..

  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: It can be rewritten as 3.2×1053.2\times10^5, whose coefficient meets the scientific-notation requirement.
  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.

It can be rewritten as 3.2×1053.2\times10^5, whose coefficient meets the scientific-notation requirement.

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