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Significant Figures

Significant Figures. The Numbers Are Speaking to Me. 6.02 x 10 23 bananas. 5.689 cm. 45,000 L. Significant Figures. Numbers give two pieces of information The numerical value The degree of certainty Example: 5 g  5 g measured to the ones place (could be between 4.5 g and 5.5 g)

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Significant Figures

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  1. Significant Figures The Numbers Are Speaking to Me 6.02 x 1023 bananas 5.689 cm 45,000 L

  2. Significant Figures • Numbers give two pieces of information • The numerical value • The degree of certainty Example: 5 g5 g measured to the ones place (could be between 4.5 g and 5.5 g) 5.000g5 g measured to the thousandths place (could be between 4.9995 g and 5.0005 g) (more certainty = more digits)

  3. 50 40 30 20 Measurement Measure as far as you can be certain and then estimate one place further Decimal place depends on instrument used We are certain that the reading is between 30 and 40oC.  3_ oC We estimate that it is a little less than half way.  34oC

  4. 5 6 7 8 5 6 7 8 Measure (in cm) to the correct number of significant figures. 6.83 cm 6.8 cm

  5. 50 40 30 20 50 • We read the thermometer at the right as 34oC. It is marked to the tens place, so we estimate to the ones. • How about now? 34.3oC (marked to ones, estimate tenths) • How about now? 40.0oC (marked to ones, estimate tenths) 40 30 20

  6. Numbers Significant does not mean important. Significant means measured. Rules 1) Non-zero numbers are significant. 95.357 g 5 SF 84.1 mL 3 SF 7 kg 1 SF

  7. Zeros Holding Decimal Place 2) Zeroes between significant figures are significant. 308 m 3 SF 1.000004 g 7 SF 400.02 L 5 SF 3) Zeroes used for spacing are NOT significant. Initial Zeros 0.0000567 g 3 SF First Measured Number Purely Decorative

  8. Zeros Between Sigfigs Zeros Holding Decimal Place Last Measured Number Zero Holding Decimal Place Final Zeroes 150 2 SF 1,000,730,000 6 SF

  9. 4) Final zeroes after a decimal point are significant. 7.300 4 SF 4.0 2 SF 150.00 5 SF 5) Zeroes between a sigfig and a decimal point are significant. 150 2 SF 150. 3 SF Lazy Principle – if it doesn’t change the mathematical value, then it must have another purpose Final Zeroes after Decimal Zero between Sigfigs

  10. 6) Exact numbers (not measured)DO NOT AFFECT sigfigs. Counting 41 cars infinite SF (Ø) 23 students infinite SF (Ø) 45 tons of cars 2 SF Conversions (by definition) 1 yard = 3 feet infinite SF (Ø) 100 cm = 1 m infinite SF (Ø)

  11. 456.01 mL 9,002 g 4,500 m 0.05 mg 25 lbs 17 pencils 0.000410 mol 4,000. yd 5 SF 4 SF 2 SF 1 SF 2 SF infinite SF (Ø) 3 SF 4 SF Practice

  12. Decimal Place Measured Digits Scientific Notation 4.975 x 1041 m The same as:497,500,000,000,000,000,000,000,000,000,000,000,000,000  4 SF Only the measured digits affect sigfigs.

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