Grade 8 Math Practice Test: Scientific Notation
- Scientific Notation
- 10 questions
- 15 minutes
This test covers writing very large and very small numbers in scientific notation and calculating with them. Tip: the first factor must be at least 1 and less than 10, so adjust the power of 10 after you multiply.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
How is 0.000507 written in scientific notation?
Correct answer: B
Move the decimal point 4 places to the right to get 5.07, so the exponent is −4. 5.7 drops the zero between 5 and 7, which changes the number.
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Question 2
What is 3.2 × 106 in standard form?
Correct answer: A
Multiplying by 106 moves the decimal point 6 places to the right: 3,200,000. 320,000 moves it only 5 places.
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Question 3
What is (4 × 105)(3 × 103) in scientific notation?
Correct answer: B
4 × 3 = 12 and 105 × 103 = 108, so 12 × 108 = 1.2 × 109. 1.2 × 108 forgets to raise the exponent when 12 becomes 1.2.
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Question 4
What is (9 × 108) ÷ (3 × 102)?
Correct answer: A
9 ÷ 3 = 3, and 108 ÷ 102 = 106 (subtract the exponents). 3 × 104 divides the exponents 8 ÷ 2 instead of subtracting.
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Question 5
What is 6.1 × 104 + 3.5 × 103?
Correct answer: D
Write both in standard form: 61,000 + 3,500 = 64,500 = 6.45 × 104. 9.6 × 104 adds 6.1 and 3.5 even though the powers of 10 are different.
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Question 6
How many times greater is 8 × 109 than 2 × 106?
Correct answer: B
8 ÷ 2 = 4 and 109 ÷ 106 = 103, so 4 × 1,000 = 4,000. 4 compares only the first factors.
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Question 7
Which number is the smallest?
Correct answer: A
The most negative exponent gives the smallest positive number: 9.1 × 10−3 = 0.0091, while 1.2 × 10−2 = 0.012. Comparing only 9.1 and 1.2 is the trap.
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Question 8
The sun is about 1.5 × 108 km from Earth, and light travels about 3 × 105 km per second. About how long does sunlight take to reach Earth?
Correct answer: D
Time = distance ÷ speed = (1.5 ÷ 3) × 103 = 0.5 × 1,000 = 500 seconds (a little over 8 minutes). 4.5 × 1013 multiplies instead of dividing.
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Question 9
A certain bacterium is 2 × 10−6 m long. How many of them placed end to end would make 1 cm (1 × 10−2 m)?
Correct answer: C
(1 × 10−2) ÷ (2 × 10−6) = 0.5 × 104 = 5,000. 2 × 10−8 multiplies the lengths instead of dividing.
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Question 10
A calculator shows 4.7E-5 as the result. What number is this?
Correct answer: C
4.7E-5 means 4.7 × 10−5. Moving the decimal point 5 places left gives 0.000047. 0.0000047 moves it 6 places.
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