1.2 Measurements and Uncertainties

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 comparison a reference point against which other things can be evaluated Ex. Meter, second, degree

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 system Metric system The science world agreed to use the International System (SI) Based upon the metric system.

1.2.1 State the fundamental units in the SI system

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

Units and Standards Ex. Length. Base unit is meter.

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)

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 names Quantity Name Quantity Symbol Unit Name Unit Symbol Area A Square meter Volume V Cubic meter Acceleration a Meters per second squared Density p Kilogram per cubic meter

Others have special names 1.2.2 Distinguish between fundamental and derived units and give examples of derived units. Others have special names Quantity Name Quantity Symbol Special unit name Special unit Symbol Frequency f Hz Force F N Energy/Work E, W J Power P W Electric Potential V

Common conversions 2.54 cm = 1 in 4 qt = 1 gallon 5280 ft = 1 mile 4 cups = 48 tsp 2000 lb = 1 ton 1 kg = 2.205 lb 1 lb = 453.6 g 1 lb = 16 oz 1 L = 1.06 qt

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.

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!

1.2.3 Convert between different units of quantities Let’s break it down. 32ft = ______in 100lbs = ______ kg 85cm = _______ in

1. 2. 4 State unites in the accepted SI format 1. 2 1.2.4 State unites in the accepted SI format 1.2.5 State values in scientific notation and in multiples of units with appropriate prefixes Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10x

The Distance From the Sun to the Earth 93,000,000 miles

Step 1 93,000,000 = 9.3000000 Move the decimal to the left Leave only one number in front of decimal 93,000,000 = 9.3000000

Step 2 Write the number without zeros 93,000,000 = 9.3

Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal Make that your power of ten 93,000,000 = 9.3 x 10 7

The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10 7

93,000,000 --- Standard Form 9.3 x 107 --- Scientific Notation

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

More Practice Problems On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011

Complete Practice Problems Write in scientific notation. 50,000 7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form Move the decimal to the right 3.4 x 105 in scientific notation 3.40000 --- move the decimal ---> 340,000 in standard form

Practice: Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 6,270,000 90,100

1.2.7 Distinguish between precision and accuracy Accuracy is how close to the “correct” value Precision is being able to repeatedly get the same value Measurements are accurate if the systematic error is small Measurements are precise if the random error is small. Examples: groupings on 4 different targets

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.

There are two types of error, random and systematic. 1.2.6 Describe and give examples of random and systematic errors. 1.2.8 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 report Can be reduced by repeating measurements many times. Measurements are precise if the random error is small

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. 1.2.8 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 method Examples – poor calibration, a consistently bad reaction time on the part of the recorder, parallax error Can be reduced by repeating measurements using a different method, or different apparatus and comparing the results, or recalibrating a piece of apparatus Measurements are accurate if the systematic error is small.

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.

Accurate or Precise?

Accurate or Precise?

Accurate or Precise?

Accurate or Precise?

1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures The numbers reported in a measurement are limited by the measuring tool  Significant figures in a measurement include the known digits plus one estimated digit

1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures The 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.

Three Basic Rules Non-zero digits are always significant. 523.7 has ____ significant figures Any zeros between two significant digits are significant. 23.07 has ____ significant figures A final zero or trailing zeros if it has a decimal, ONLY, are significant. 3.200 has ____ significant figures 200 has ____ significant figures

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 ________ 0.0156 oz ________

Exact Numbers Can be thought of as having an infinite number of significant figures An exact number won’t limit the math. 1. 12 items in a dozen 2. 12 inches in a foot 3. 60 seconds in a minute

Example Video 4:45

Multiplying and Dividing Round to so that you have the same number of significant figures as the measurement with the fewest significant figures.  42 two sig figs x 10.8 three sig figs 453.6  answer 450 two sig figs

Practice: Multiplying and Dividing In each calculation, round the answer to the correct number of significant figures. A. 2.19 X 4.2 = 1) 9    2) 9.2   3) 9.198  B. 4.311 ÷ 0.07 =           1) 61.58    2) 62   3) 60

Adding and Subtracting Base your answer on which number column is lacking significance.      25 + 1.34 26.34  Calculated Answer 26 Rounded answer based on sig figs

Practice: Adding and Subtracting In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 =           1) 256.75  2) 256.8  3) 257     B. 58.925 - 18.2 =           1) 40.725  2) 40.73  3) 40.7 
 

1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures Practice How many sig figs are in each number listed? A) 10.47020 D) 0.060 B) 1.4030 E) 90210 C) 1000 F) 0.03020 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

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 = 3217.94g Calculate the density of the house brick and give your answer to an appropriate number of sig figs.

1.2.9 Practice 13(Dickinson) Solution Density = (mass/volume) Density = 1.8320808 g cm-3 Density = 1.8 g cm-3

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.

Analogue instruments = +/- half of the limit of reading 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties. Rule of Thumb Analogue instruments = +/- half of the limit of reading Ex. Meter stick’s limit of reading is 1mm so it’s uncertainty range is +/- 0.5mm Digital instruments = +/- the limit of the reading Ex. Digital Stopwatch’s limit of reading is 0.01s so it’s uncertainty range is +/- 0.01s

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 uncertainties Absolute uncertainties are constants associated with a particular measuring device. (Ratio) Fractional uncertainty = absolute uncertainty measurement Percentage uncertainties = fractional x 100%

Example A meter rule measures a block of wood 28mm long. Absolute = 28mm +/- 0.5mm Fractional = 0.5mm = 28mm +/- 0.0179 28mm Percentage = 0.0179 x 100% = 28mm +/- 1.79%

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.