1. Measuring and Recording Data

2. developed in France in 1795 a.k.a. “SI”-International System of Units a.k.a. “SI” - International System of Units The U.S. was (and still is) reluctant to “go metric.” very costly to change very costly to change perception of “Communist” system perception of “Communist” system natural resistance to change natural resistance to change American pride American pride

3. The SI unit of: length is the meter, m length is the meter, m time is the second, s time is the second, s mass is the kilogram, kg. mass is the kilogram, kg. electric charge is the Coulomb, C electric charge is the Coulomb, C temperature is the degree Kelvin, K temperature is the degree Kelvin, K an amount of a substance is the mole, mol an amount of a substance is the mole, mol luminous intensity is the candle, cd luminous intensity is the candle, cd

4. The second is defined in terms of The second is defined in terms of atomic vibrations of Cesium-133 atoms. The meter is defined in terms of the speed of light. The meter is defined in terms of the speed of light. The kilogram is still defined by The kilogram is still defined by an official physical standard. “Derived units” are combinations of these “fundamental units” Examples include speed in m/s, area in m 2, force in kg. m/s 2, acceleration in m/s 2, volume in m 3, energy in kg. m 2 /s 2

5. 10 18 exa E 10 15 peta P 10 12 tera T 10 9 giga G 10 9 giga G 10 6 mega M 10 6 mega M 10 3 kilo k 10 3 kilo k 10 2 hecto h 10 2 hecto h 10 1 deka da 10 1 deka da 10  18 atto a 10  15 femto f 10  12 pico p 10  9 nano n 10  9 nano n 10  6 micro  10  6 micro  10  3 milli m 10  3 milli m 10  2 centi c 10  2 centi c 10  1 deci d 10  1 deci d

6. Explore the metric system at link1, link2, and link3. link1link2link3link1link2link3 See definitions of metric units here. here Click here to do conversions. here

7. There is no such thing as absolute certainty of a scientific claim. The validity of a scientific conclusion is always limited by: the experiment the experiment design, equipment, etc... the experimenter the experimenter human error, interpretation, etc... our limited knowledge our limited knowledge ignorance, future discoveries, etc...

8. All measurements have some degree of uncertainty. Precision single measurement exactness, definiteness single measurement - exactness, definiteness group of measurements agreement, closeness together group of measurements - agreement, closeness together Accuracy closeness to the accepted value % error = accepted - observed accepted x 100%

9. Four student lab groups performed data collection activities in order to determine the resistance of some unknown resistor (you will do this later in the course). Data from 5 trials are displayed below. Suppose the accepted value for the resistance is 500 Ω. Then we would classify each groups’ trials as: Group 1: neither precise nor accurate Group 2: precise, but not accurate Group 3: accurate, but not precise Group 4: both precise and accurate Example of the differences between precision and accuracy for a set of measurements: Group Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 avg 13461278126413132.6 2126127126128125126.4 32050062980938500 4502501503498499500.6

10. The precision, or decimal place, to which a single measurement is recorded is determined by the graduations of the measuring device. The rule is simple: You record what you know for certain, and then estimate one more decimal position. For example, if a device is marked by tens, you record to the if a device is marked by tens, you record to the ones place ones place if a device is marked by hundredths, you record to if a device is marked by hundredths, you record to the thousandths the thousandths if a measurement is recorded to the hundredths, if a measurement is recorded to the hundredths, the device used must have been marked by the device used must have been marked by tenths, etc… tenths, etc…

11. Example: This thermometer is marked every 10 degrees. We know for certain that the temperature measurement is between 40 and 50 degrees, so it is “forty- something”. That “something” is what we estimate, and is the last decimal place recorded. Therefore it would be appropriate to call this reading 42 or 43 degrees, but not 43.5 degrees. “If marked by tens, you record to the ones.”

12. Example: Suppose that a weight measurement taken using an analog scale (not digital) is recorded as 168.4 pounds. This reading implies that the scale used must have been calibrated, or marked, by what increments? Since the weight is recorded to the tenth of a pound, this means that the value in the tenth’s place must be an estimate. The scale had to have been marked in such a way that the measurement was known to be between 168 and 169 pounds. This implies that there must have been markings for 168 and 169, so the scale was marked by pounds (the one’s place). “If recorded to the tenths, it was marked by ones.”

14. 1. All non-zero digits are significant. 2. Zeros between other significant digits are significant. are significant. 3. Leading zeros are not significant. 4. Final zeros before the decimal are not significant. significant.

15. Operations with Significant Digits Addition and Subtraction round the sum or difference to the least precise decimal place Multiplication and Division round so that the product or quotient has a total number of significant digits equal to the total number of significant digits of the least precise quantity

16. Learn more about significant digits herehere and here. here Check your understanding here. here The “bottom line” is that the precision to which a measured or calculated amount is written provides valuable information as to the precision (certainty) of that value and the device used to measure it.