1. Sig Figs The Saga

2. In a galaxy far, far away, a bunch of students were arguing whether there was a difference between two measurements. 20.4 cm and 20.40 cm

3. Reading measuring instruments to their limit You can only be as precise as your measuring instrument allows you to be. Ex.

4. Other examples: How much fluid is in this graduated cylinder? (73.0 ml) What is the temperature? (38.45 o C)

5. What are Significant Figures? (as opposed to significant figurines...)

6. Sig figs help us understand how precise measurements are. Using sig figs increases accuracy and precision. Sig figs cut down on error caused by improper rounding. HOORAY FOR SIG FIGS!!! SIG FIGS RULE

7. So… which digits are significant?significant Rule #1: – All non-zero digits are significant. 24 has two sig figs, 24.1 has 3 sig figs Rule #2: – All zeros bounded by non-zero integers are significant 2004 has four sig figs 20.04 also has 4 sig figs

8. So… which digits are significant?significant Rule #3: –Zeros placed before other digits (leading zeros) are not significant 0.024 has 2 sig figs Rule #4: –Zeros at the end of a number are significant ONLY if they come after a decimal point 2.40 has three sig figs 240 only has 2 sig figs

9. Practice: How many sig figs? »409.25o 0.050 »83o 300 900 »98.207o 5.5 x 10 2 »0.001o 45.030 »4.3 x 10 2 o 35 000 »0.003050o 0.00400 »4200o 16.8090 »0.9106o 460 090 »0.200o 150 000 000

10. Rules for Addition and Subtraction In an addition or subtractions, – answers must be rounded to the same decimal place (not sig figs) as the least number of decimal places in any of the numbers being added or subtracted –Ex. 2.42 + 14.2 + 0.6642

11. Step 1 line them up 2.42 14.2 +0.6642 17.2842 Step 2: round to 3.3, because 0.2 only has one decimal place The answer is 17.3

12. Ex 1- 6.25 + 4.350 + 15.809 = 26.409 becomes 26.41WHY Ex 2- 14.4 + 12.0 - 5 = 21.4 becomes 21WHY

13. Ex 3- 589.090 + 0.04 + 78.890 = 668.02 becomes 668.02 WHY Ex 4- 33.2306 + 5.050 + 0.00604 = 38.28664 becomes 38.287 WHY

14. Rules for Multiplication and Division The number of sig figs in the answer should be the same as in the number with the least sig figs being multiplied or divided. –Ex. 7.3 x 1264 = 9227.2 »The answer must only contain 2 sig figs, so we use scientific notation »The answer becomes 9.2 x 10 3 »This answer contains 2 sig figs

15. Ex 1- 15.0 x 4.515 x 1376 = 931 896 becomes 9.32 x 10 5 WHY Ex 2- 0.003 x 0.050 x 0.04 = 0.000006 becomes 0.000006 = 6 x 10 -6 WHY

16. Ex 3- 45.56 x 134.04 x 0.340 = 2076.333216 becomes 2.08 x10 3 WHY Ex 4- 34.56 x 14 x 134.020 = 64844.2368 becomes 6.5 x 10 4 WHY

17. Adding and multiplying numbers in a word problem 1- Set up numbers according to the word problem 2- Solve using order of operations 3- At each step give the answer in sig figs 4- Convert final answer to sig figs

18. Ex 1. 4.67 + 8.953 + 0.652 765.32 x 8.9 -4.67 + 8.953 + 0.652 = 14.275 becomes 14.28 -765.32 x 8.9 = 6811.348 becomes 6.8 x 10 3 -14.28/6.8 x 10 3 = 0.0021 becomes 0.0021 = 2.1x10 -3

19. Ex 26.8 + 5.80 x 8.0 x 0.06 - 7.870 0.0800 -6.8 +(5.80 x 8.0 x 0.06) - 7.870 0.0800 -6.8 + (2.784) - 7.870 which becomes 0.0800 -6.8 + 3 – 7.870 0.0800 - 1.93 which becomes 0.0800 2 0.0800 = 25 becomes 30 why

20. Exceptions and special circumstances

21. Adding and scientific notation (5.8 x 10 2 ) + 368 4.87 x 10 5 When adding in using SN, the exponents must be the same. You have 2 options to solve the problem. 1- Convert 5.8 x10 2 to 580 and get rid of the exponent 580 + 368 2- Convert 368 to the same exponent so it becomes 3.68 x 10 2 5.8 x 10 2 + 3.68 x 10 2 Both are correct, but option 1 is easier

22. Rounding off and keeping a zero as a significant digit 8253.0569 = 649.847 12.7 In this example you must keep 3 sig figs in your answer. When rounding off 649.847 should become 650. Problem, 650 only has 2 sig figs Solution: put a – above the zero, this makes it significant, 650 will become your answer.

23. Having many insignificant zero’s and addition When adding the following:136.2 + 2 500 000 + 14.01 We get 2 500 150.21 which should become 2 500 150. EXCEPT, we have to use sig figs, and the addition rule says that we must round to the least precise decimal place. Therefore, because 2 500 000 is only precise to the hundred thousands place, we need to round the answer to 2 500 000. This is true for any additions that end in non sig. zero’s. ex- 5 500 + 15 = 55 15 but becomes 5500 310 + 6 = 316 but becomes 320 259 500 + 1670 + 23 = 261 193 but becomes 261 200

24. Converting units When converting units, sig figs need to be maintained. Ex 1- 4.0 cm to m becomes 0.040 not 0.04 Ex 2- 1250 mL becomes 1.25 L not 1.250

25. Solve the following: 5.3 x 4.2 + 1.50 2.5 + 8.163 x 5.67 (5.3 x 4.2) + 1.50 = (22.26) + 1.50 = 2.5 + (8.163 x 5.67)2.5 + (46.28421) 22 + 1.50 = 23.50 becomes 2.5 + 46.3 48.8 24 = 0.4918032 which becomes 48.8 0.49

26. (6.42 x 10 5 ) x (0.45 x 10 -3 ) + 56.5 + 150.03 (6.42 x 10 5 ) x (0.45 x 10 -3 ) + 56.5 + 150.03 = (288.9) + 56.5 + 150.03 = (2.8 x 10 2 ) + 56.5 + 150.03 = 280 + 56.5 + 150.03 = 486.53 which becomes 487 which becomes 490 Holy cow, zero’s have become the enemy!!

27. Your next assignment is hand in a 2000word essay on the history and importance of significant figures and how they positively affect our everyday lives. Due date- 2 weeks

28. Psych- Why would I want to correct 96 essays on significant figures?????