1. Significant Figures… Bluefield High School 1

2. What is a significant digit? Significant digits is a set of internationally accepted rules for measurement. The rule of thumb is to record all digits that are certain, plus one that is estimated. The rules of significant digits apply to all reporting and calculating unless you are dealing with defined values (those by definition. For example …60 minutes = 1 hour).

3. 1. Every nonzero digit is significant. 24.7 has three significant digits 2. Zeroes between nonzero digits are significant. 2.07m and 109m each have three significant digits. 3. Zeroes in front of all nonzero digits are not significant. They are merely place holders. The measurements of 0.00037m and 0.46m each have two significant digits. 4. Zeroes at the end of the number and to the right of the decimal point are significant. The measurement 43.00m, 1.010m and 9.500m all have four significant digits. 5. Zeroes at the end of a measurement and to the left of the decimal point are unclear. You may consider all such zeroes to be not significant. To avoid confusion, express the number in scientific notation. The Rules of Significant Digits…

4. When to use Significant figures When a measurement is recorded only those digits that are dependable are written down.

5. When to use Significant digits… If you measured the width of a paper with your ruler you might record 21.7cm. To a mathematician 21.70, or 21.700 is the same.

6. But, to a scientist 21.7cm and 21.70cm is NOT the same 21.700 cm to a scientist means the measurement is accurate to within one thousandth of a cm. significant figures video

7. How many sig digits? 7 40 0.5 0.00003 7 x 10 5 7,000,000 1 1 1 1 1 1

8. How many sig digits here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4

9. How many sig digits here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6

10. Counting Significant Figures Number of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb___ 122.55 m___ All non-zero digits in a measured number are (significant or not significant). 10

11. Leading Zeros Number of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb____ 0.000262 mL ____ Leading zeros in decimal numbers are (significant or not significant). 11

12. Sandwiched Zeros Number of Significant Figures 50.8 mm3 2001 min4 0.702 lb____ 0.00405 m ____ Zeros between nonzero numbers are (significant or not significant). 12

13. Trailing Zeros Number of Significant Figures 25,000 in. 2 200 yr1 48,600 gal3 25,005,000 g ____ Are trailing zeros, serving as place holders in numbers without decimals, significant or not significant? 13

14. Learning Check A. Which answer contains 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5 14

15. Solution A. Which answers contain 3 significant figures? 2) 0.00476 3) 4760 B. All the zeros are significant in 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 2) 535,000 3) 5.35 x 10 5 15

16. Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000 16

17. Solution … 3) 0.000015 and 150,000 17

18. Learning Check State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7 18

19. Solution A. 0.030 m2 B. 4.050 L4 C. 0.0008 g1 D. 3.00 m 3 E. 2,080,000 bees3 19

20. Significant Numbers in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing 20

21. Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place 21

22. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7 22

23. Solution A. 235.05 + 19.6 + 2.1 = 2) 256.8 B. 58.925 - 18.2= 3) 40.7 23

24. Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. 24

25. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041 25

26. Solution A. 2.19 x 4.2 = 2) 9.2 B. 4.311 ÷ 0.07 = 3) 60 C. 2.54 x 0.0028 = 2) 11 0.0105 x 0.060 Continuous calculator operation = 2.54 x 0.0028  0.0105  0.060 26

27. Significant Figures 1.8 Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x 3.6666 = 16.536366= 16.5 3 sig figsround to 3 sig figs 6.8 ÷ 112.04 = 0.0606926 2 sig figsround to 2 sig figs = 0.061

28. Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise but not accurate & not precise 1.8

29. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

30. The Distance From the Sun to the Earth 93,000,000

31. Step 1 Move decimal left Leave only one number in front of decimal

32. Step 2 Write number without zeros

33. Step 3 Count how many places you moved decimal Make that your power of ten

34. The power of ten is 7 because the decimal moved 7 places.

35. 93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

36. Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

37. More Practice Problems 1) 734,000,000 = ______ x 10 8 2) 870,000,000,000 = ______x 10 11 3) 90,000,000,000 = _____ x 10 10 On these, decide where the decimal will be moved. 1)7.34 x 10 8 2) 8.7 x 10 11 3) 9 x 10 10

38. Complete Practice Problems 1) 50,000 2) 7,200,000 3) 802,000,000,000 Write in scientific notation. 1) 5 x 10 4 2) 7.2 x 10 6 3) 8.02 x 10 11

39. Scientific Notation to Standard Form Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form 3.40000 --- move the decimal

40. Write in Standard Form 6.27 x 10 6 9.01 x 10 4 tutorial 6,270,000 90,100

41. 1.9 Dimensional Analysis Method of Solving Problems 1.Determine which unit conversion factor(s) are needed 2.Carry units through calculation 3.If all units cancel except for the desired unit(s), then the problem was solved correctly. 1 L = 1000 mL How many mL are in 1.63 L? 1L 1000 mL 1.63 L x = 1630 mL 1L 1000 mL 1.63 L x = 0.001630 L2L2 mL

42. The speed of sound in air is about 343 m/s. What is this speed in miles per hour? 1 mi = 1609 m1 min = 60 s1 hour = 60 min 343 m s x 1 mi 1609 m 60 s 1 min x 60 min 1 hour x = 767 mi hour meters to miles seconds to hours 1.9

43. Please do the following questions… Page 349 in your text… #’s 2,3,4,5,6,8 and 9 43