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Significant figures

Significant figures. Review. Counting Significant Figures. All non zero digits are significant Example: 7.89 has 3 significant figures 0.789 has 3 significant figures. Counting Significant Figures. Zeros between non-zero digits are significant. Example: 4505 has 4 significant figures

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Significant figures

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  1. Significant figures Review

  2. Counting Significant Figures • All non zero digits are significant • Example: • 7.89 has 3 significant figures • 0.789 has 3 significant figures

  3. Counting Significant Figures • Zeros between non-zero digits are significant. • Example: • 4505 has 4 significant figures • 20.789 has 5 significant figures

  4. Counting Significant Figures • Zeros to the right of the decimal point are significant • Example: • 7.00 has 3 significant figures • 0.78900 has 5 significant figures

  5. Counting Significant Figures • Zeros between a non-zero number and a decimal point are significant • Example: • 700. has 3 significant figures • 700.0 has 4 significant figures

  6. Counting Significant Figures Practice 1. 4.50 2. 6005 3. 7000 4. 670. 5. 670

  7. Rounding • If the digit to be dropped is greater than 5, then add 1 to the last digit to be retained and drop all digits to the right • Example: • 5.788 is rounded to 5.79 if 3 significant figures are required • 5.788 is rounded to 5.8 if 2 significant figures are required

  8. Rounding • If the digit to be dropped is less than 5, simply drop it without adding any number to the last digit • Example: • 5.733 is rounded to 5.73 if 3 significant figures are required • 5.733 is rounded to 5.7 if 2 significant figures are required

  9. Rounding • When the digit to be dropped is exactly 5, round to the nearest even number • Example: • 5.755 is rounded to 5.76 if 3 significant figures are required • 5.785 is rounded to 5.8 if 2 significant figures are required

  10. Rounding Practice 1. 3.05 to two significant figures 2. 2.4675 to four significant figures 3. 4.67 to two significant figures 4. 5.63 to two significant figures 5. 7.005 to two significant figures

  11. Addition and Subtraction • The answer will be the same precision as the least precise measurement • Example: • 4.67 + 1.3249 = 5.9949 • After rounding = 5.99

  12. Multiplication and Division • The answer will contain the same number of significant figures as the number used in calculating with the least number of significant figures • Example: • 5.3 x 1.234 = 6.5402 • After rounding = 6.5

  13. Practice 1. 394.540 g + 198.9916 g = 2. 35 g/ 10.1 mL = 3. 1161 x 10^6 J/0.034 s = 4. 0.076 mm - 0.12 mm = 5. 456.0 cm + 1.34 cm + 200. cm = 6. 22 m/s x 40 s = 7. 34298.0 g + 24.340 g = 8. 202 m/ 234 s =

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