Name ——————————————————————— SECTION 6 Date ———————————— Algebra Lesson 4: Scientific Notation Scientific notation is a way to write very small or very large numbers using powers of 10. The table shows some powers of 10. Power of 10 Value 10−2 10−1 100 101 102 103 0.001 0.01 0.1 1 10 100 1000 Write 9,100,000 in scientific notation. HINT Move the decimal point as needed to get a number that is at least 1, but less than 10. 9,100,000 Move the decimal point 6 places to the left. 9.1 3 106 EXAMPLE 2 Use 6 as an exponent of 10. Write 0.0000005 in scientific notation. HINT Use positive exponents for large numbers. Use negative exponents for small numbers. 0.0000005 Move the decimal point 7 places to the right. 5 3 10 Copyright © by McDougal Littell, a division of Houghton Mifflin Company. −7 EXAMPLE 3 Use 27 as an exponent of 10. 6. ALGEBRA 4. Scientific Notation EXAMPLE 1 10−3 Write 2.3 3 104 in standard form. 23,000 The exponent of 10 is 4. Move the decimal point 4 places to the right. EXAMPLE 4 Write 8 3 10−5 in standard form. 0.00008 The exponent of 10 is 25. Move the decimal point 5 places to the left. Practice: First Try Write the power of 10 that makes a true statement. 1. 8,000,000 5 8 3 _____ 2. 450,000 5 4.5 3 _____ 3. 0.00006 5 6 3 _____ 4. 0.000000077 5 7.7 3 _____ 5. 380,000,000 5 3.8 3 _____ 6. 0.00092 5 9.2 3 _____ McDougal Littell Middle School Math Remediation Book Lesson 6.4 173 Name ——————————————————————— Date ———————————— Practice: Second Try Write the number in scientific notation. 1. 87,000,000 2. 5,000,000,000 3. 4. 926,000 5. 0.0000015 6. 0.0000008 8. 0.000000398 9. 0.0000031 6. ALGEBRA 4. Scientific Notation 7. 0.0009 420,000 Write the number in standard form. 10. 5.9 3 106 11. 4.58 3 104 12. 9.0 3 102 13. 4 3 108 14. 7.5 31025 15. 8.2 3 1026 16. 1.82 3 1024 17. 3 3 1029 18. 5.5 3 1023 Give a complete answer. 19. In the year 2005, a company made a profit of about $3.8 3 105. In 2006, the company made about $40,000. In which year did the company make a greater profit? Explain. 20. The size of Specimen A is 5 3 1024 cm. The size of Specimen B is 0.00055 cm. Which specimen is smaller? Explain. 21. Explain why each number is not written in scientific notation. a. 41 3 103 b. 0.3 3 1027 Puzzle The mass of Earth is about 6 trillion trillion kilograms. Write this number! Standard Notation 174 McDougal Littell Middle School Math Remediation Book Lesson 6.4 Scientific Notation Copyright © by McDougal Littell, a division of Houghton Mifflin Company. Extend Your Skills !NSWER+EY -iVÌÊÈÊ}iLÀ> iÃÃÊ{ÊÊ««°Ê£ÇÎ£Ç{® *À>VÌVi\Ê ÀÃÌÊ/ÀÞÊÊÊ £°ÊÊÓ°ÊÊÎ°ÊÊ{° -iV`Ê/ÀÞÊÊÊ £°ÊÊÓ°ÊÊÎ°ÊÊ{°ÊÊÊx°ÊÊÊÊ È°ÊÊÇ°ÊÊÊn°ÊÊ°ÊÊ£ä°ÊÊÊ££°ÊÊÊÊ £Ó°ÊÊ£Î°ÊÊ£{°ÊÊÊ£x°ÊÊ£È°ÊÊÊ £Ç°£n°ÊÊÊ £°)NTHATYEARTHEYMADEABOUTWHICHISGREATERTHANÊÊÊ Óä°3PECIMEN!4HATSPECIMENISCMWHICHISSMALLERTHANCM Ó£>°ISNOTINSCIENTIlC NOTATION BECAUSE IS NOT LESS THAN Ó£L°ISNOTINSCIENTIlC NOTATION BECAUSE IS NOT GREATER THAN OR EQUAL TO ÊÊ *Õââi Name ——————————————————————— SECTION 6 Date ———————————— Algebra Lesson 4: Scientific Notation Scientific notation is a way to write very small or very large numbers using powers of 10. The table shows some powers of 10. Power of 10 Value 10−2 10−1 100 101 102 103 0.001 0.01 0.1 1 10 100 1000 Write 9,100,000 in scientific notation. HINT Move the decimal point as needed to get a number that is at least 1, but less than 10. 9,100,000 Move the decimal point 6 places to the left. 9.1 3 106 EXAMPLE 2 Use 6 as an exponent of 10. Write 0.0000005 in scientific notation. HINT Use positive exponents for large numbers. Use negative exponents for small numbers. 0.0000005 Move the decimal point 7 places to the right. 5 3 10 Copyright © by McDougal Littell, a division of Houghton Mifflin Company. −7 EXAMPLE 3 Use 27 as an exponent of 10. 6. ALGEBRA 4. Scientific Notation EXAMPLE 1 10−3 Write 2.3 3 104 in standard form. 23,000 The exponent of 10 is 4. Move the decimal point 4 places to the right. EXAMPLE 4 Write 8 3 10−5 in standard form. 0.00008 The exponent of 10 is 25. Move the decimal point 5 places to the left. Practice: First Try Write the power of 10 that makes a true statement. 1. 8,000,000 5 8 3 _____ 2. 450,000 5 4.5 3 _____ 3. 0.00006 5 6 3 _____ 4. 0.000000077 5 7.7 3 _____ 5. 380,000,000 5 3.8 3 _____ 6. 0.00092 5 9.2 3 _____ McDougal Littell Middle School Math Remediation Book Lesson 6.4 173 Name ——————————————————————— Date ———————————— Practice: Second Try Write the number in scientific notation. 1. 87,000,000 2. 5,000,000,000 3. 4. 926,000 5. 0.0000015 6. 0.0000008 8. 0.000000398 9. 0.0000031 6. ALGEBRA 4. Scientific Notation 7. 0.0009 420,000 Write the number in standard form. 10. 5.9 3 106 11. 4.58 3 104 12. 9.0 3 102 13. 4 3 108 14. 7.5 31025 15. 8.2 3 1026 16. 1.82 3 1024 17. 3 3 1029 18. 5.5 3 1023 Give a complete answer. 19. In the year 2005, a company made a profit of about $3.8 3 105. In 2006, the company made about $40,000. In which year did the company make a greater profit? Explain. 20. The size of Specimen A is 5 3 1024 cm. The size of Specimen B is 0.00055 cm. Which specimen is smaller? Explain. 21. Explain why each number is not written in scientific notation. a. 41 3 103 b. 0.3 3 1027 Puzzle The mass of Earth is about 6 trillion trillion kilograms. Write this number! Standard Notation 174 McDougal Littell Middle School Math Remediation Book Lesson 6.4 Scientific Notation Copyright © by McDougal Littell, a division of Houghton Mifflin Company. Extend Your Skills