2 1.2.1 State the fundamental units in the SI system In science, numbers aren’t just numbers.They need a unit. We use standards for this unit.A standard is:a basis for comparisona reference point against which other things can be evaluatedEx. Meter, second, degree
3 1.2.1 State the fundamental units in the SI system The unit of a #, tells us what standard to use.Two most common system:English systemMetric systemThe science world agreed to use the International System (SI)Based upon the metric system.
4 1.2.1 State the fundamental units in the SI system
5 1.2.1 State the fundamental units in the SI system Conversions in the SI are easy because everything is based on powers of 10
6 Units and StandardsEx. Length.Base unit is meter.
7 1.2.2 Distinguish between fundamental and derived units and give examples of derived units. A derived unit is a unit which can be defined in terms of two or more fundamental units.For example speed(m/s) is a unit which has been derived from the fundamental units for distance(m) and time(s)
8 Some derived units don’t have any special names 1.2.2 Distinguish between fundamental and derived units and give examples of derived units.Some derived units don’t have any special namesQuantity NameQuantity SymbolUnit NameUnit SymbolAreaASquare meterVolumeVCubic meterAccelerationaMeters per second squaredDensitypKilogram per cubic meter
9 Others have special names 1.2.2 Distinguish between fundamental and derived units and give examples of derived units.Others have special namesQuantity NameQuantity SymbolSpecial unit nameSpecial unit SymbolFrequencyfHzForceFNEnergy/WorkE, WJPowerPWElectric PotentialV
10 Common conversions 2.54 cm = 1 in 4 qt = 1 gallon 5280 ft = 1 mile 4 cups = 48 tsp2000 lb = 1 ton1 kg = lb1 lb = g1 lb = 16 oz1 L = 1.06 qt
11 1.2.3 Convert between different units of quantities Convert your age into seconds.Most people can do that if given a few minutes. But do you know what you were doing.Write what you know.
12 1.2.3 Convert between different units of quantities Let’s break it down.Write what you know.The unit you are coming from goes on bottom.The unit you are going to is placed on top.Multiply on the top and bottom and simplify!
13 1.2.3 Convert between different units of quantities Let’s break it down.32ft = ______in100lbs = ______ kg85cm = _______ in
14 1. 2. 4 State unites in the accepted SI format 1. 2 1.2.4 State unites in the accepted SI format State values in scientific notation and in multiples of units with appropriate prefixesScientific NotationA short-hand way of writing large numbers without writing all of the zeros.
15 Scientific notation consists of two parts: A number between 1 and 10A power of 10N x 10x
16 The Distance From the Sun to the Earth 93,000,000 miles
17 Step 1 93,000,000 = 9.3000000 Move the decimal to the left Leave only one number in front of decimal93,000,000 =
18 Step 2Write the number without zeros93,000,000 = 9.3
19 Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal Make that your power of ten93,000,000 = 9.3 x 107
20 The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 107
22 Practice Problem -----> -----> -----> -----> Write in scientific notation.Decide the power of ten.98,500,000 = 9.85 x 10?64,100,000,000 = 6.41 x 10?279,000,000 = 2.79 x 10?4,200,000 = 4.2 x 10?9.85 x 107----->6.41 x 1010----->2.79 x 108----->----->4.2 x 106
23 More Practice Problems On these, decide where the decimal will be moved.734,000,000 = ______ x 108870,000,000,000 = ______x 101190,000,000,000 = _____ x 1010Answers3) 9 x 10107.34 x 1082) 8.7 x 1011
24 Complete Practice Problems Write in scientific notation.50,0007,200,000802,000,000,000Answers1) 5 x 1042) 7.2 x 1063) 8.02 x 1011
25 Scientific Notation to Standard Form Move the decimal to the right3.4 x 105 in scientific notationmove the decimal--->340,000 in standard form
26 Practice: Write in Standard Form Move the decimal to the right.6.27 x 1069.01 x 1046,270,00090,100
27 1.2.7 Distinguish between precision and accuracy Accuracy is how close to the “correct” valuePrecision is being able to repeatedly get the same valueMeasurements are accurate if the systematic error is smallMeasurements are precise if the random error is small.Examples: groupings on 4 different targets
28 Example of precision and accuracy A voltmeter is being used to measure the potential difference across an electrical component. If the voltmeter is faulty in some way, such that it produces a widely scattered set of results when measuring the same potential difference, the meter would have low precision. If the meter had not been calibrated correctly and consistently measured 0.1V higher than the true reading (zero offset error), it would be in accurate.
29 There are two types of error, random and systematic. 1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced.There are two types of error, random and systematic.Random Errors - occur when you measure a quantity many times and get lots of slightly different readings.Examples - misreading apparatus, Errors made with calculations, Errors made when copying collected raw data to the lab reportCan be reduced by repeating measurements many times.Measurements are precise if the random error is small
30 1. 2. 6 Describe and give examples of random and systematic errors. 1 1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced.There are two types of error, random and systematic.Systematic error – when there is something wrong with the measuring device or methodExamples – poor calibration, a consistently bad reaction time on the part of the recorder, parallax errorCan be reduced by repeating measurements using a different method, or different apparatus and comparing the results, or recalibrating a piece of apparatusMeasurements are accurate if the systematic error is small.
31 Graphs can be used to help us identify different types of error. Low precision is represented by a wide spread of points around an expected value.Low accuracy is represented by an unexpected intercept on the y-axis. Low accuracy gives rise to systematic errors.
36 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figuresThe numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit
37 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figuresThe number of sig figs should reflect the precision of the value of the input data.If the precision of the measuring instrument is not known then as a general rule, give your answer to 3 sig figs.
38 Three Basic Rules Non-zero digits are always significant. 523.7 has ____ significant figuresAny zeros between two significant digits are significant.23.07 has ____ significant figuresA final zero or trailing zeros if it has a decimal, ONLY, are significant.3.200 has ____ significant figures200 has ____ significant figures
39 Practice How many sig. fig’s do the following numbers have? 38.15 cm _________5.6 ft ____________2001 min ________50.8 mm _________25,000 in ________200. yr __________0.008 mm ________oz ________
40 Exact NumbersCan be thought of as having an infinite number of significant figuresAn exact number won’t limit the math.1. 12 items in a dozen2. 12 inches in a foot3. 60 seconds in a minute
42 Multiplying and Dividing Round to so that you have the same number of significant figures as the measurement with the fewest significant figures. two sig figsx three sig figs453.6 answer450 two sig figs
43 Practice: Multiplying and Dividing In each calculation, round the answer to the correct number of significant figures.A X 4.2 =1) 9 2) 9.2 3) 9.198 B ÷ 0.07 = 1) 2) 62 3) 60
44 Adding and Subtracting Base your answer on which number column is lacking significance. 2526.34 Calculated Answer26 Rounded answer based on sig figs
45 Practice: Adding and Subtracting In each calculation, round the answer to the correct number of significant figures.A = 1) 2) 256.8 3) 257 B = 1) 2) 40.73 3) 40.7
46 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figuresPracticeHow many sig figs are in each number listed?A) D) 0.060B) E) 90210C) F)Calculate, giving the answer with the correct number of sig figs.12.6 x 0.53(12.6 x 0.53) – 4.59(25.36 – 4.1) ÷ 2.317
47 1.2.9 Practice 13(Dickinson)A meter rule was used to measure the length, height and thickness of a house brick and a digital balance was used to measure its mass. The following data were obtained.Length = 20.5cm, height = 8.4cm, thickness 10.2cm, mass = gCalculate the density of the house brick and give your answer to an appropriate number of sig figs.
48 1.2.9 Practice 13(Dickinson) Solution Density = (mass/volume) Density = g cm-3Density = 1.8 g cm-3
49 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties. Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.
50 Analogue instruments = +/- half of the limit of reading State uncertainties as absolute, fractional and percentage uncertainties.Rule of ThumbAnalogue instruments = +/- half of the limit of readingEx. Meter stick’s limit of reading is 1mm so it’s uncertainty range is +/- 0.5mmDigital instruments = +/- the limit of the readingEx. Digital Stopwatch’s limit of reading is 0.01s so it’s uncertainty range is +/- 0.01s
51 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties. We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertaintiesAbsolute uncertainties are constants associated with a particular measuring device.(Ratio) Fractional uncertainty = absolute uncertaintymeasurementPercentage uncertainties = fractional x 100%
52 Example A meter rule measures a block of wood 28mm long. Absolute = mm +/- 0.5mmFractional = 0.5mm = mm +/28mmPercentage = x 100% =28mm +/- 1.79%
53 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties. Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.