2Biblical ReferenceHe measured its wall and it was 144 cubits thick, by man's measurement, which the angel was using.Revelation 21:17
3Accuracy vs. Precision For a single measurement: Accuracy - An indication of how close a measurement is to the accepted valuePrecision - An indication of the degree of exactness of a measurementFor multiple measurements:Accuracy - An indication of how close the average measurement is to the accepted valuePrecision - An indication of the agreement among a number of similar measurements
4Accuracy – measurement of closeness to the true value of a number
5Precision – measure of how close a series of measurements are to one another
6Scientific Notation: 602,000,000,000,000,000,000,000 copper atoms 6.02 x 1023 copper atomsgrams3.27 x gramsOnly 1 digit to the left of the decimal place.
7Significant Figures:When you make a measurement there is some estimationRecorded numbers in a measurement or calculation are called significant figuresWhat is the length of the black line in cm?How many significant figures are in the measurement?
8Number of Significant Figures = 2 You can't always keep all the digits a calculator produces. You can only keep the significant ones, the ones that are not beyond the accuracy of the measuring device. These digits are called significant digits or figures.Length cmNumber of Significant Figures = 2
9Significant Figure Rules : Non zeros count (123.34) – 5 Sig Figs2. Leading zeros do NOT count (0.004) – 1 Sig Fig3. Captive zeros count (2004, 2.004, 20.04) – 4 Sig Figs4. Trailing zeros count IF there is a decimal point (20., 20.00, 0.200) – 2, 4, and 3 Sig Figs
10Significant Figures in Calculations: A calculated answer cannot be more precise than the least precise measurement from which it was calculatedRoundingIf the last number is less than 5, round downIf the last number is greater than 5, round upIf the last number is a 5, round so that the rounded number is even.
11Mathematical Operations: Rounding with Addition and SubtractionRound to the least number of decimal placesExample: = 11.0Rounding with Multiplication and DivisionRound to the same number of significant figures as the measurement with the least number of significant figuresExample: 540. g / 62 ml = 8.7 g/ml
12Determining Error:Accepted value – correct value based on reliable referencesExperimental value – value measured in labError = Accepted Value – Experimental valuePercent Error = |Error| x 100Accepted Value*|Error| is the absolute value of the error
13SI units Measurements are fundamental to the experimental sciences Science uses the International System of Measurements (SI)MKS and CGS
14Measuring with SI Units - MKS QuantitySI Base UnitSymbolLengthmetermMasskilogramkgTemperatureKelvinKTimesecondsAmount of substancemolemolLuminous intensitycandelacdElectric currentampereA
15Metric Prefixes Prefix Meaning Factor mega (M) 1 million times larger than preceding106kilo (k)1000 times larger than preceding103deci (d)10 times smaller than preceding10-1centi (c)100 times smaller than preceding10-2milli (m)1000 times smaller than preceding10-3micro (m)1 million times smaller than preceding10-6nano (n)1 billion times smaller than preceding10-9pico (p)1 trillion times smaller than preceding10-12
16Metric Units of Length Unit Relationship Example Kilometer (km) 1 km = 103 mFive city blocksMeter (m)Base unitHeight of doorknobDecimeter (dm)101 dm = 1 mLarge orangeCentimeter (cm)102 cm = 1 mShirt buttonMillimeter (mm)103 mm = 1 mThickness of dimeMicrometer (mm)106 mm = 1 mDiameter of bacteriaNanometer (nm)109 nm = 1 mThickness of RNA
21Metric Units of Temperature The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C.The Kelvin scale sets 0 at absolute zero.The units of Kelvin and Celsius are equivalentK = °C°C = K –
28A conversion factor is a ratio that, when multiplied by the item you are converting, cancels out the units you do not want and leaves you with the units you want.Dimensional Analysis is a technique where you use the dimensions/units to check if a relationship is correct.
31Conversion Factor Steps Step 1 – Determine what units you are given and what units you need.Step 2 – Determine what conversion factors you need to use.Step 3 – Arrange the conversion factors so that the units you do not want cancel out.Step 4 – Make sure your last unit is the unit need.
32Conversion Examples 500 cm ´ 1 m = 5 m 100 cm 6 cm ´ 10 mm = 60 mm 8 h60 min60 sec=28,800 s1 h1 min
33Example Problem With sig figs K2 is the world’s second tallest peak at 8000 m. What is the height of K2 in feet?With sig figs
34Dimensional Analysis Question The period (T) of oscillation of a simple pendulum depends upon the acceleration of gravity(g) and the length (L) of the pendulum.Which expression below represents the relationship between T, g and L?