CHAPTER 9 : Motion Physics Intro to MEASUREMENTS SIGNIFICANT FIGURES SCIENTIFIC NOTATION CALCULATIONS ACCURACY AND PRECICION ERRORS REVIEW OF METRIC SYSTEM
Significant figures and calculations
Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated.
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.
Two special situations have an unlimited number of Significant figures: 1.. Counted items a) 23 people, or 425 thumbtacks 2 Exactly defined quantities b) 60 minutes = 1 hour
Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 100,890 L 3.29 x 10 3 s 0.0054 cm 3,200,000 ml 5 dogs 4 sig figs 5 sig figs 3 sig figs 2 sig figs unlimited 2 sig figs This is a counted value
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
Make the following have 3 sig figs: M 761.50 14.334 10.44 10789 8024.50 203.514 762 14.3 10.4 10800 8020 204
Significant Figures Using 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 3 is the rounding number, and drop every number behind
Examples 1. 6.8 + 11.934 =18.734 18.7 (3 sig figs) 2. 89.332 + 1.1 = 90.432 round off to 90.4 3. 3.70-2.9133 = 0.7867
Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem.
Scientific Notation
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.
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.
Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10 x
Changing standard form to scientific notation.
EXAMPLE 5 500 000 =
EXAMPLE #2 0.0075 = Numbers less than 1 will have a negative exponent.
EXAMPLE #3 CHANGE SCIENTIFIC NOTATION TO STANDARD FORM 2.35 x 10 8
EXAMPLE #4 9 x 10-5
TRY THESE Express in scientific notation 1) 421.96 2) 0.0421 3) 0.000 56 4) 467 000 000
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.
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.
TRY THESE Change to Standard Form 1) 4.21 x 10 5 2) 0.06 x 10 3 3) 5.73 x 10-4 4) 4.321 x 10-5
If you can t round to the correct number of significant figures using standard form.try scientific notation!! Not usually done but can get out of a sig. fig. bind!!
Metric Conversions Ladder Method
KILO 1000 Units 1 2 HECTO 100 Units Ladder Method DEKA 10 Units Meter s Liters Gram How do you use the ladder method? s 1 st Determine your starting point. 2 nd Count the jumps to your ending point. 3 rd Move the decimal the same number of jumps in the same direction. 3 DECI 0.1 Unit CENTI 0.01 Unit MILLI 0.001 Unit How to use Exponent Method If getting bigger X 10 # of jumps If getting smaller 10 # of jumps
Conversion Practice 1000 mg = g 1 L = ml 160 cm = mm 14 km = m 109 g = kg 250 m = km Compare using <, >, or =. 56 cm 6 m 7 g 698 mg
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
Converting Units (Derived Units) Ex: Convert 100 km/hr to m/s A Conversion like this must be done using multiple conversion factors! We need to convert hours into minutes and then minutes into seconds; then convert Km to m
Converting m\s to km\h
Area Changing around formulas to solve for certain values
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
Types of Errors Random errors- the same error does not repeat every time. Blunders Human Error
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.
Accuracy vs Precision π Accuracy Precision 3 NO NO 7.18281828 NO YES 3.14 YES NO 3.1415926 YES YES
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 )