CHAPTER 1 : MEASUREMENTS

1. CHAPTER 1 : MEASUREMENTS • SIGNIFICANT FIGURES AND • CALCULATIONS

2. Significant figures and calculations

3. Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated.

4. Significant Figures • •Any digit that is not zero is significant 2.234 kg 4 significant figures • •Zeros between non-zero digits are significant. 607 m 3 significant figures • • Leading zeros (to the left) are not significant. 0.07 L 1 significant figure. 0.00520 g 3 significant figures • Trailing ( to the right) only count if there is a decimal in the number. 5.0 mg 2 significant figures. 50 mg 1 significant figure.

5. Two special situations have an unlimited number off Significant figures: • 1.. Counted items a) 23 people, or 425 thumbtacks 2 Exactly defined quantities b) 60 minutes = 1 hour

6. Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 mL 2 sig figs 5 dogs unlimited This is a counted value

7. Rounding Calculated Answers • Decide how many significant figures are needed • Round to that many digits, counting from the left • Is the next digit less than 5? Drop it. • Next digit 5 or greater? Increase by 1 • 3.016 rounded to hundredths is 3.02 • • 3.013 rounded to hundredths is 3.01 • • 3.015 rounded to hundredths is 3.02 • • 3.045 rounded to hundredths is 3.04 • • 3.04501 rounded to hundredths is 3.05

8. Addition and Subtraction • The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem. Examples: 4.8 -3.965 0.835 0.8 1 decimal places 3 decimal places

9. Make the following have 3 sig figs: 762 • M 761.50 • 14.334 • 10.44 • 10789 • 8024.50 • 203.514 14.3 10.4 10800 8020 204

10. Multiplication and Division • Round the answer to the same number of significant figures as the least number of significant figures in the problem.

11. Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 13 (2 sig figs)

12. Addition and Subtraction: The number of decimal places in the result equals the number off decimalplaces in the least precise measurement. • 6.8 + 11.934 =18.734 18.7 (3 sig figs) • 89.332 + 1.1 = 90.432 round off to 90.4 • one significant figure after decimal point • 3.70 -2.9133 = 0.7867 two significant figures after decimal point round off to 0.79

13. Scientific Notation

14. What is scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise.

15. Why use scientific notation? • For very large and very small numbers, these numbers can expressed in a more concise form. • Numbers can be used in a computation with far greater ease.

16. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

17. Changing standard form to scientific notation.

18. EXAMPLE • 5 500 000 • = 5.5 x 106 We moved the decimal 6 places to the left. A number between 1 and 10

19. EXAMPLE #2 Numbers less than 1 will have a negative exponent. • 0.0075 • = 7.5 x 10-3 We moved the decimal 3 places to the right. A number between 1 and 10

20. EXAMPLE #3 • CHANGE SCIENTIFIC NOTATION TO STANDARD FORM 2.35 x 108 = 2.35 x 100 000 000 = 235 000 000 Standard form Move the decimal 8 places to the right

21. EXAMPLE #4 9 x 10-5 = 9 x 0.000 01 = 0.000 09 Standard form Move the decimal 5 places to the left

22. TRY THESE • Express in scientific notation • 1) 421.96 • 2) 0.0421 • 3) 0.000 56 • 4) 467 000 000

23. TRY THESE • Change to Standard Form • 1) 4.21 x 105 • 2) 0.06 x 103 • 3) 5.73 x 10-4 • 4) 4.321 x 10-5

24. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

25. Continued… • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

26. Types of Errors • Random errors- the same error does not repeat every time. • • Blunders • • Human Error

27. Systematic Errors • – These are errors caused by the way in which the experiment was conducted. In other words, they are caused by flaws in equipment or experimental. • Can be discovered and corrected.

28. Examples: You measure the mass of a ring three times using the same balance and get slightly different values: 12.74 g, 12.72 g, 12.75 g. ( random error ) The meter stick that is used for measuring, has a millimetre worn off of the end therefore when measuring an object all measurements are off. ( systematic error )

29. Accuracy or Precision • Precision Reproducibility of results Several measurements afford the same results Is a measure of exactness • Accuracy How close a result is to the “true” value Is a measure of rightness

30. Accuracy vs Precision

31. Metric Conversions Ladder Method

32. 1 2 3 MetersLitersGrams How do you use the “ladder” method? 1st – Determine your starting point.2nd – Count the “jumps” to your ending point.3rd – Move the decimal the same number of jumps in the same direction. Starting Point Ending Point __. __. __. 2 3 1 Ladder Method KILO1000Units HECTO100Units DEKA10Units DECI0.1Unit CENTI0.01Unit MILLI0.001Unit 4 km = _________ m How many jumps does it take? 4. = 4000 m

33. Compare using <, >, or =. 56 cm 6 m 7 g 698 mg Conversion Practice Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm 14 km = _______ m 109 g = _______ kg 250 m = _______ km

34. Metric Conversion Challenge Write the correct abbreviation for each metric unit. 1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____ 2) Meter _____ 5) Millimeter _____ 8) Centimeter _____ 3) Gram _____ 6) Liter _____ 9) Milligram _____ Try these conversions, using the ladder method. 10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm 11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km 12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg 13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm 14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g