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The Fundamental Tools

The Fundamental Tools. Of Science. Units. Some fundamental measurements in all of science: Length Time Mass Many others are combinations of these: Energy, Speed, Volume, Area. Units. International Standard Units (SI, aka metric) Length (m – meter) Mass (kg – kilogram)

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The Fundamental Tools

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  1. The Fundamental Tools Of Science

  2. Units • Some fundamental measurements in all of science: • Length • Time • Mass • Many others are combinations of these: • Energy, Speed, Volume, Area

  3. Units • International Standard Units (SI, aka metric) • Length (m – meter) • Mass (kg – kilogram) • Time (s – seconds) • Energy (J – joules) • Temperature (K – kelvin)

  4. Temperature Scales 212 ˚F 100 ˚C 373 K 100 K 180˚F 100˚C 32 ˚F 0 ˚C 273 K Fahrenheit Celsius Kelvin Boiling point of water Freezing point of water Notice that 1 kelvin degree = 1 degree Celsius

  5. Temperature Scales 100 oF 38 oC 311 K oF oC K

  6. Significant Figures: Digits in a measurement having values that are known with certainty plus one digit having a value that is estimated.

  7. Reading Volume: Significant Figures on an Instrument

  8. Measurements that contain a greater number of significant figures are more precise than measurements that contain fewer significant figures. • Always select an instrument that gives you the most significant figures. Only report as many sig figs as that instrument allows

  9. The Rules

  10. All numbers 1-9 are significant. Zeros are sometimes significant, here's how you can tell: If a decimal point is present, starts on the Pacific side, move across until you get to a 1-9 digit, and start counting to the end If a decimal point is absent, start on the Atlantic side, move across until you get to a 1-9 digit, and start counting to the end 1.100 has ? sig figs, 0.00540 has ?, 40.01 has ? 1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ?

  11. When multiplying or dividing measurements: round the answer to the same number of digits as the measurement having the fewest number of significant figures. When adding or subtracting measurements: round the answer to the same number of decimal places as the measurement having the fewest number of decimal places.

  12. Higher precision 123456.7890 • Identify the LEAST PRECISE measurement. • Identify the MOST PRECISE digit (place) within that measurement. • Round the answer to this digit (place). Lower precision

  13. Conversion • Commonly Used Prefixes: • kilo = 1000 of something ( 1km= 1000m, kg) • deci =0.1 of something (10 dm = 1m) • centi = 0.01 of something (100 cm = 1m) • milli = 0.001 of something (103 mm = 1m) • micro = 0.000001 (106µm = 1m) • nano = 0.000000001 (109 nm = 1m) • pico = 0.000000000001 (1012 pm = 1m) Refer to Conversion Chart to additional prefixes

  14. Conversion • All conversion factors are fractions. 100 cm 100 cm 1 m 100 cm = = 1 1 km 103 m 103 m 103 m = = 1 1m 10-6µm 1m 10-6µm = = 1

  15. The Nature of Units • Units are multiplied and divided like numbers are. 10 meters 2 meters = 5 (the units cancel out) 10 meters x 10 meters x 10 meters = 103 m3 (the units combine as exponents) 50 miles 10 gallons = 5 miles/gallon (the units combine as a fraction) • Only IDENTICAL UNITS on 2 numbers can be added or subtracted. • The answer always has the same units. 100 kg – 25 kg = 75 kg 100 kg – 25 m = Meaningless Dribble

  16. How many seconds are in 54 days? • Write the measurement with its unit. • If it isn’t already a fraction, write it over 1. • Set up conversion factors that • Cancel units you want to get rid of • Replace with units you are looking for • Have values on the top and bottom that are equivalent • Multiply numbers across the top • Multiply numbers across the bottom • Divide to get answer, check units

  17. Scientific Notation • 10000000000000000000000 • 0.00000000000000000000000000001 • There has to be a better way to write those numbers • Rules for scientific notation • 1) Always express the number starting with the one’s place followed by any decimal digits, times a power of 10. • 2)To express a large number, count the number of decimal places needed to move to the one’splace, and make that number the exponent of ten. • 3) To express a very small number, count the number of decimal places needed to move to the one’s place, and make that number the NEGATIVE exponent of ten. • 4) After re-expressing the number in scientific notation, check it by writing out the expanded ten, and multiply it by the measured number.

  18. Scientific Notation • Examples: 0.000000000000000000000000000000001 = 1.0 x 10-35 94140000000000000000000000000000000 = 9.414 x 1035

  19. Accuracy Precision What's the difference??

  20. Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise

  21. Instruments are... Accurate if calibrated to a standard Precise if they give many significant digits

  22. Percent Error To report the accuracy of your measurements Observed – True True X 100

  23. Average Deviation To report the precision of your measurements 1 Average your measurements 2 Find the absolute values of the differences between each measurement and the average 3 Average these differences

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