* 100.5 = 3.16 (rounding value)

* e.g. 4,200,000=4.2*106

* since 4.2 > 3.16 the magnitude is 107 (6 is rounded up)

The SI System of Fundamental and Derived Units

* Fundamental SI Units:

Quantity| SI Unit| SI Symbol|

length| meter| m|

mass| kilogram| kg|

time| second| s|

electric current| ampere| A|

thermodynamic temperature| Kelvin| K|

amount of substance| mole| m|

luminous intensity| candela| cd|

* Derived SI Units

Quantity| SI Unit| SI Symbol| Fundamental SI Units involved| frequency| hertz| Hz| s-1|

force| Newton| N| kg*m*s-2|

work/energy| joule| J| kg*m2*s-2|

power| watt| W| kg*m2*s-3|

pressure| Pascal| Pa| kg*m-1*s-2|

charge| coulomb| C| A*s|

potential difference| volt| V| kg*m2*s-3*A-1|

resistance| ohm| Ω| kg*m2*s-3*A-2|

Systematic and Random Errors

* Systematic error

* Affects each measurement the same way

* Error by system

* E.g. lack of calibration (zero error)

* E.g. Wrong theory or equation

* Not accurate

* Random error

* Different for each measurement

* By human error or environmental influence

* E.g. temperature variation

* E.g. Not enough data collected

* Not precise

* Accuracy – how close the results are from the true value * Indicated by relative or percentage error

* Precision – how the different results vary from each other * Indicated by absolute error

* Reduce random error

* Consistent experimental procedure

* Choose instrument with higher degree of accuracy

* Reduce variation (air current, temperature variation, vibration…) * Systematic error corrected before the experiment

Significant Figures

* Used to indicate degree of accuracy of precision in a measurement * Rules for significant figures:

* All non-zero digits are significant

* All zeros between two non-zero digits are significant * For numbers less than one, zeros directly after the decimal point are NOT significant * A zero to the right of a point and following a non-zero digit is significant * All other zeros are NOT significant

* When adding and subtracting a series of measurements, the least accurate place value in the answer can only be stated to the same number of significant figures as the measurement of the series with the least number of decimal places. * When multiplying and dividing a series of measurements, the number of significant figures in the answer should be equal to the least number of significant figures in any of the data of the series. * When rounding off a number, if the digit following the required rounding off digits is 4 or less, you maintain the last reportable digit and if it is six or more you increase the last reportable digit by one. If it is a five followed by more digits except an immediate zero, increase the last reportable digit. If there is only five with no digits following, increase reportable odd digits by one and maintain reportable even digits.

Absolute, Fractional and Percentage Uncertainties

* Maximum degree of uncertainty is half the limit of reading * Uncertainties are given in 1sf

Meter ruler| ± 0.05 cm|

Vernier capilers| ± 0.005 cm|

Micrometer screw gauge| ± 0.005 mm|

50 cm3 measuring cylinder| ± 0.2 cm3|

10 cm3 measuring cylinder| ± 0.1 cm3|

Electric balance| ± 0.005 g|

Watch hand second| ± 0.5 s|

Digital timer| ± 0.0005 s|

Spring balance (0-20N)| ± 0.1 N|

Resistor| ± 2%|

* Example: 0.40 ± 0.1

* Absolute uncertainty is the size of an error and its units * 0.1 cm

* Not always maximum degree of uncertainty

* Fractional uncertainty is the absolute uncertainty divided by the measurement. * 0.10.4

* It has no units

* Percentage uncertainty is relative uncertainty given in...