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 m 3 significant figures• Leading zeros (to the left) are not significant L 1 significant figure.g 3 significant figuresTrailing ( 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 itemsa) 23 people, or 425 thumbtacks2 Exactly defined quantitiesb) 60 minutes = 1 hour
6 Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs17.10 kg4 sig figs100,890 L5 sig figs3.29 x 103 s3 sig figscm2 sig figs3,200,000 mL2 sig figs5 dogsunlimitedThis is acounted value
7 Rounding Calculated Answers Decide how many significant figures are neededRound to that many digits, counting from the leftIs the next digit less than 5? Drop it.Next digit 5 or greater? Increase by 13.016 rounded to hundredths is 3.02• rounded to hundredths is 3.01• rounded to hundredths is 3.02• rounded to hundredths is 3.04• 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:4.8-3.9651 decimal places3 decimal places
9 Make the following have 3 sig figs: 762M14.33410.441078914.310.4108008020204
10 Multiplication and Division Round the answer to the same number of significant figures as the least numberof 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 = (2 sig figs)
12 Addition and Subtraction: The number of decimal places in the result equals the number off decimal places in the least precise measurement.= (3 sig figs)= round off to 90.4one significant figure after decimal point= two significant figures after decimal point round off to 0.79
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 10A power of 10N x 10x
18 EXAMPLE= 5.5 x 106We moved the decimal 6 places to the left.A number between 1 and 10
19 EXAMPLE #2Numbers less than 1 will have a negative exponent.0.0075= 7.5 x 10-3We 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 =Standard formMove 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)4)
23 TRY THESE Change to Standard Form 1) 4.21 x 105 2) 0.06 x 103
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 ErrorsRandom 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: g, g, 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 • Accuracy Reproducibility of resultsSeveral measurements afford the sameresultsIs a measure of exactness• AccuracyHow close a result is to the “true” valueIs a measure of rightness
30 Accuracy vs Precision π Accuracy Precision 3 NO 7.18281828 YES 3.14
32 How many jumps does it take? Ladder Method123KILO 1000 UnitsHECTO 100 UnitsDEKA 10 UnitsDECI 0.1 UnitMeters Liters GramsCENTI 0.01 UnitMILLI UnitHow 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.4 km = _________ mStarting PointEnding PointHow many jumps does it take?4.1__.2__.3__.= 4000 m
33 Conversion Practice Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL cm = _______ mm14 km = _______ m 109 g = _______ kg 250 m = _______ kmCompare using <, >, or =.56 cm m g mg
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 ) 16 cm = _______ mm11) 104 km = _______ m 16) 198 g = _______ kg ) 2500 m = _______ km12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g