Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Scientific Notation and Significant Digits In scientific notation, a number has the form a 3 10 n, where n is an integer and 1 # a , 10. 1 EXAMPLE Write 5.59 3 10 6 in standard form. 5.59 3 10 6 = 5 590 000 A positive exponent indicates a value greater than 1. Move the decimal point six places to the right. = 5, 590, 000 2 EXAMPLE Write 0.000 031 8 in scientific notation. 0.0000318 = 3.18 3 10-5 Move the decimal point to create a number between 1 and 10 (five places to the right). Since the original number is less than 1, use a negative exponent. When a measurement is in scientific notation, all the digits of the number between 1 and 10 are significant digits. When you multiply or divide measurements, your answer should have as many significant digits as the least number of significant digits in any of the numbers involved. 3 EXAMPLE Multiply A 6.71 3 108 mi/h B and A 3.8 3 104 h B . A 6.71 3 10 8 mi/h B A 3.8 3 10 4 h B = = = < three significant digits 4 two significant digits EXAMPLE 10 5 22 6.332 3 1.6 3 10 (6.71 ? 3.8)(10 8 ? 10 4 B 25.498 3 10 12 2.5498 3 10 13 2.5 3 10 13 mi Rearrange factors. Add exponents when multiplying powers of 10. Write in scientific notation. Round to two significant digits. 5 Simplify 6.332 3 10 22 . 1.6 3 10 5 - (-2) = 6.332 1.6 3 10 Subtract exponents when dividing powers of 10. = 3.9575 3 10 7 < 4.0 3 10 7 Simplify. Round to two significant digits. EXERCISES Change each number to scientific notation or to standard form. 1–10. See margin. 1. 1,340,000 2. 6.88 3 10-2 3. 0.000775 4. 0.0072 5. 1.113 3 10 5 6. 8.0 3 10-4 7. 1895 8. 2.3 3 10 3 9. 123,400 10. 7.985 3 10 4 Write each product or quotient in scientific notation. Round to the appropriate number of significant digits. 11–22. See margin. 11. A 1.6 3 10 2 B A 4.0 3 10 3 B 5 14. 7.0 3 10 3 2.89 3 10 17. A 1.78 3 10 -7 B A 5.03 3 10 -5 B 20. A 3.95 3 10 4 B 4 A 6.8 3 10 8 B 854 Skills Handbook 12. A 2.5 3 10 -3 B A 1.2 3 10 4 B 4 15. 1.4 3 10 2 8.0 3 10 18. A 7.2 3 10 11 B A 5 3 10 6 B 21. A 4.9 3 10 -8 B 4 A 2.7 3 10 -2 B 13. A 4.237 3 10 4 B A 2.01 3 10 -2 B 6 16. 6.48 3 105 3.2 3 10 19. A 8.90 3 10 8 B 4 A 2.36 3 10 -2 B 22. A 3.972 3 10 -5 B A 4.7 3 10 -4 B