Units, Measurement, Significant Figures & Conversions

1. Units, Measurement, Significant Figures & Conversions Physics

2. SI Units • The SI Units we will be concerned with mostly are: Quantity Unit Length/Distance Time Mass Temperature meter [m] second [s] kilogram [kg] Kelvin [K]

3. SI Units • All of our other units will be based on meters, kilograms, seconds, and Kelvins. • This is referred to as the mks unit system • Other systems: cgs; ft/lb/s

4. Making Measurements • All measurements must contain both • A number • A unit • Measured values are reported such that only the last digit is uncertain. • ALL digits of a measurement, including the last one, are called significant figures. Aka: Sig figs

5. Measuring Length • Length measurements are made in units of meters.

6. Length Measurements 10 11 12 13 14  What is the measurement? A) 12.92 m B) 12 m C) 12.9 m

7. Length Measurements 10 11 12 13 14  What is the measurement? A) 10.3 m B) 10.28 m C) 10 m

8. Length Measurements 10 11 12 13 14  What is the measurement? A) 11.5 m B) 11.55 m C) 11 m

9. Sig Fig Rules • All nonzero digits are significant. • Ex: 2.54 has ____ sig figs • Ex: 167.965 has ____ sig figs Zero Rules • A zero is significant when it appears between two nonzero digits • Ex: 2.04 has ____ sig figs • Ex: 10.065 has ____ sig figs 3 6 3 5

10. Sig Fig Rules Zero Rules cont. • A zero is significant when it appears at the end of a number AND to the right of the decimal • Ex: 4.900 has ____ sig figs • Ex: 17.0 has ____ sig figs 4 3

11. Sig Fig Rules Zero Rules cont. • A zero isNEVER significant when it appears in front of a number • Ex: 0.007865 has ____ sig figs • Ex: 0.09 has ____ sig fig 4 1

12. Sig Fig Rules Zero Rules cont. • A zero isSOMETIMES significant when it appears at the end of a number AND to the left of the decimal For this course, assume these zeros ARE NOT significant unless you read “precisely” or “exactly” in front of the number • Ex: 20 has ____ sig fig • Ex: 3400 has ____ sig figs 1 2

13. Sig Fig Rules A good rule-of-thumb for the zeros in sig figs is this: • Convert the number to scientific notation and if the zeros drop out then they are not significant • Ex: 0.007865 = 7.865 x 10-3 So it has 4 sig figs • Ex: 3400 = 3.4 x 102 So it has 2 sig figs

14. Try it! How many sig figs are in each of the following? • 0.000743 A) 3 B) 6 C) 7

15. Try it! How many sig figs are in each of the following? • 0.000743 • 10.47 A) 2 B) 3 C) 4

16. Try it! How many sig figs are in each of the following? • 0.000743 • 10.47 • 219,976.900 A) 5 B) 9 C) 11

17. Try it! How many sig figs are in each of the following? • 0.000743 • 10.47 • 219,976.900 • 4.00000009 A) 2 B) 8 C) 9

18. Try it! How many sig figs are in each of the following? • 0.000743 • 10.47 • 219,976.900 • 4.00000009 • 0.0072 A) 2 B) 4 C) 5

19. Accuracy & Precision • Two types of numbers in scientific work: • Exact numbers • Inexact numbers • Measurements are inexact due to equipment and human error. • Precision & accuracy are used to describe the uncertainty of measured values.

20. Accuracy & Precision • Precision refers to how reproducible individual measurements are • Accuracy refers to how closely individual measurements agree with the “true” or accepted value

21. Accuracy & Precision Accurate but not precise Precise but not accurate

22. Accuracy & Precision Neither accurate nor precise Both accurate and precise GOOD BAD

23. Unit Conversions • Notes on board

24. Try It! 183 cm equals how many meters? First, choose a conversion factor: A) B) C) Then do the calculation: A) 1.83 m B) 18.3 m C) 18300 m 10 mm 1 cm 1 m 100 cm 1,000 m 1 km

25. Try It! 8,700 milligrams is how many grams? First, choose a conversion factor: A) B) C) Then do the calculation: A) 0.87g B) 87.0 g C) 8.7 g 1000 kg 1 g 1000 mg 1 g 1 g 1000 mg

26. Try It! 4.3 Astronomical Units (A.U.) is equal to how many kilometers? First, choose a conversion factor: A) B) C) Then do the calculation: A) 6.4 km B) 6.432 x 108 km C) 6.4 x 108 km 149,597,870.7 km 1 A.U. 1 A.U. 149,597,870.7 km 149,597.8707 m 1 A.U.