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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? ________________________________________________________________________________________ ________________________________________________________________________________________ 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) _______________________ ________________________ ________________________ _______________________ ________________________ ________________________ 5. (2.9 × 105) + (8.4 × 104) 104) 6. (1.8 × 103)(3.4 × 108) 7. (3.024 × 109) ÷ (5.4 × _______________________ ________________________ ________________________ _______________________ ________________________ ________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 1 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 ____________________________________________ ____________________________________________ 3. 3.3 × 109 + 2.6 × 109 + 7.7 × 108 4. 8.0 × 104 − 3.4 × 104 − 1.2 × 103 ____________________________________________ ____________________________________________ 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? ________________________________________________________________________________________ 14. How many strides would it take to finish the first half of the marathon? Hint: Write 5 ft as 5.0 × 100 ________________________________________________________________________________________ and 4.5 feet as 4.5 × 100. 15. How many strides would it take to finish the second half of the marathon? ________________________________________________________________________________________ 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. 2