1. Significant Figures Chemistry I

2. Significant Figures The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit

3. Counting Significant Figures RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding occurred. Number of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb___ 122.55 m___

4. Leading Zeros RULE 2. Leading zeros in decimal numbers are NOT significant. Number of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb____ 0.000262 mL 0.000262 mL ____

5. Sandwiched Zeros RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they are on an end of a number.) Number of Significant Figures 50.8 mm3 2001 min4 0.702 lb____ 0.00405 m ____

6. Trailing Zeros RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. Number of Significant Figures 25,000 in. 2 200. yr3 48,600 gal____ 25,005,000 g ____

7. Learning Check A A. Which answers contain 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

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

9. 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 Learning Check

10. 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

11. 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

12. 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

13. 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.

14. 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

15. Reading a Meterstick. l 2.... I.... I 3....I.... I 4.. cm First digit (known)= 2 2.?? cm Second digit (known)= 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported=2.75 cm or2.74 cm or2.74 cm or2.76 cm

16. Known + Estimated Digits In 2.76 cm… Known digits 2 and 7 are 100% certain The third digit 6 is estimated (uncertain) In the reported length, all three digits (2.76 cm) are significant including the estimated one

17. Learning Check. l 8.... I.... I 9....I.... I 10.. cm What is the length of the line? 1) 9.6 cm 2) 9.62 cm 3) 9.63 cm How does your answer compare with your neighbor’s answer? Why or why not?

18. Zero as a Measured Number. l 3.... I.... I 4.... I.... I 5.. cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is 5.00 cm

19. What is a significant figure?  There are 2 kinds of numbers: Exact: the amount of money in your account. Known with certainty.

20. What is a significant figure? Approximate: weight, height—anything MEASURED. No measurement is perfect.

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

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

23. When to use Significant figures 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.

24. But, to a scientist 21.7cm and 21.70cm is NOT the same  21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

25. But, to a scientist 21.7cm and 21.70cm is NOT the same  If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

26. How do I know how many Sig Figs?  Rule: All digits are significant starting with the first non-zero digit on the left. Ex: 7.5 or 0.5  You can have as many decimals as you want on the left of the decimal Ex: 0.05 OR 00.05 OR 000.05

27. How do I know how many Sig Figs?  Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

28. How many sig figs?  7  40  0.5  0.00003  7 x 10 5  7,000,000 11 11 11 11 11 11

29. How do I know how many Sig Figs?  2 nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

30. How do I know how many Sig Figs?  3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

31. How do I know how many Sig Figs?  3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

32. How many sig figs here?  1.2  2100  56.76  4.00  0.0792  7,083,000,00 0 22 22 44 33 33 44

33. How many sig figs here?  3401  2100  2100.0  5.00  0.00412  8,000,050,00 0 44 22 55 33 33 66

34. What about calculations with sig figs?  Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

35. Add/Subtract examples  2.45cm + 1.2cm = 3.65cm,  Round off to = 3.7cm  7.432cm + 2cm = 9.432 round to  9cm

36. Multiplication and Division  Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

37. A couple of examples  56.78 cm x 2.45cm = 139.111 cm 2  Round to  139cm 2  75.8cm x 9.6cm = ?

38. The End Have Fun Measuring and Happy Calculating!