Download Operations with Scientific Notation

Name _______________________________________ Date __________________ Class __________________
LESSON
2-4
Operations with Scientific Notation
When completing mathematical operations with integers, there are
procedures that simplify the process.
Problem 1
You can add or subtract numbers in scientific notation.
(5.9 × 105) − (5.4 × 104)
5
5
(5.9 × 10 ) − (0.54 × 10 )
5
(5.9 − 0.54) × 10
5.36 × 105
← Check to see if each power of 10 has the same exponent.
← Adjust to get the same exponent.
← Add or subtract the decimal parts.
Use 10 to the common power.
← Check that the answer is in scientific notation.
Problem 2
You can multiply or divide numbers in scientific notation.
(3.5 × 108) × (9.1 × 104)
(3.5 × 9.1) ×(108 × 104)
8+4
(3.5 × 9.1) × 10
31.85 × 1012
13
3.185 × 10
← Regroup so decimals and powers of 10 are grouped.
← Multiply or divide the decimal parts.
If multiplying, add exponents. If dividing, subtract exponents.
← Check that the answer is in scientific notation.
← Answer in scientific notation.
Complete.
1. When is scientific notation most useful?
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Compute. Write each answer in scientific notation.
2. (1.43 × 105) ÷ (2.6 × 102)
3. (2.8 × 106) − (1.3 × 106)
4. (5.8 × 106)(2.5 × 103)
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5. (2.9 × 105) + (8.4 × 104)
104)
6. (1.8 × 103)(3.4 × 108)
7. (3.024 × 109) ÷ (5.4 ×
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name _______________________________________ Date __________________ Class __________________
LESSON
2-4
Operations with Scientific Notation
Practice and Problem Solving: A/B
Add or subtract. Write your answer in scientific notation.
1. 6.4 × 103 + 1.4 × 104 + 7.5 × 103
2. 4.2 × 106 − 1.2 × 105 − 2.5 × 105
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3. 3.3 × 109 + 2.6 × 109 + 7.7 × 108
4. 8.0 × 104 − 3.4 × 104 − 1.2 × 103
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Multiply or divide. Write your answer in scientific notation.
5. (3.2 × 108)(1.3 × 109) = _________________
6.
8.8 × 107
= _________________
4.4 × 104
7. (1.5 × 106)(5.9 × 104) = _________________
8.
1.44 × 1010
= _________________
2.4 × 102
Write each number using calculator notation.
9. 4.1 × 104 = _________________
10. 9.4 × 10−6 = _________________
Write each number using scientific notation.
11. 5.2E–6 = _________________
12. 8.3E+2 = _________________
Use the situation below to complete Exercises 13–16. Express each
answer in scientific notation.
A runner tries to keep a consistent stride length in a marathon. But, the
length will change during the race. A runner has a stride length of 5 feet for
the first half of the race and a stride length of 4.5 feet for the second half.
13. A marathon is 26 miles 385 yards long. That is about 1.4 × 105 feet.
How many feet long is half a marathon?
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14. How many strides would it take to finish the first half of the marathon?
Hint: Write 5 ft
as 5.0 × 100
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and 4.5 feet as
4.5 × 100.
15. How many strides would it take to finish the second half of the marathon?
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16. How many strides would it take the runner to complete marathon?
Express your answer in both scientific notation and standard notation.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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