2: Measurements and Calculations

Scientific notation Used when dealing with very large or very small numbers 1 atom of gold =0.000 000 000 000 000 000 000 327g 1g of H =602,000,000,000,000,000,000,000 atoms 300,000,000 m/sec =Speed of light 0.000 000 000 000 753 g = mass of a dust particle

How to Write in Scientific Notation 123,000,000,000  1.23 x 10 11 coefficient base exponent Put the decimal after the first digit and drop the zeroes. The coefficient will be 1.23 The base is always 10 To find the exponent count the number of places from the decimal to the end of the number.

Scientific notation On your calculator: Practice: 0.00000000245 548,000,000,000 3.67 X 105 2.98 X 10-3 On your calculator: Use EE or EXP button to mean “X 10” 2.98 X 10-3  2.98 EE -3 (2.98 X 10-3)(7.62 X 105) = ? ?=2271  2.27 X 103 2.45 X 10-9 5.48 X 1011 367000 0.00298

Practice Convert to scientific notation Convert to standard notation 45700 0.0096 24212000 0.0000655 Convert to standard notation 4.5 x 10-5 2.1 x 104 6.33 x 108 2.98 x10-3

Measurement No human endeavor can be called science if it cannot be demonstrated mathematically Leonardo da Vinci (1452-1519)

Observations Qualitative Quantitative

SI (Système Internationaled’Unités) International System of Units Base units kg kilogram mass m meter length mol mole amount s second time K Kelvin temperature A Ampere electric current cd candela luminous intensity

Derived SI Units m2 area m3 volume g/m3, g/cm3 density J (Joule) energy J = kg m2 s2

Non-SI Units L Liter Volume °C Celcius Temperature g/mL Density atm atmosphere Pressure

Why use metric system? 98% world uses it Used throughout scientific community Easier- less memorizing Uses powers of ten Applies to all types measurements What is the next smaller size wrench? Powers of ten video

Metric Prefixes Used to make unit smaller or bigger mega M kilo k deci d centi c milli m micro  nano n pico p

Questions If I went to the mall what unit would I use to measure the distance? If I was measuring the length of a cell what unit would I use? m, km, mm, cm, nm, m

Complete 1kg= ________g 1m= ________cm 1s= ________ps 1km= ________m 1g= ________ng 1cal= _______dcal 1m= _________m 1MJ = ________J 1L = _______mL

Metric Match Kg mg ms μg μm m Mg

Metric-U.S. Conversions Need to know some metric-US relationships: 1 in = 2.54 cm 1 L = 1.06 quarts 1 kg = 2.2 lbs.

Volume measurements m3, cm3, dm3 L, mL 1L= 1000mL 1mL = 1cm3 Space something takes up L x H x W Units: m3, cm3, dm3 L, mL Know relationship 1L= 1000mL 1mL = 1cm3 1 sugar cube = 1cm3 20drops water = 1mL

Equipment used to measure volume

Mass Weight = force that measures the pull on a given mass by gravity Mass = measure of the quantity of matter SI unit is the Kilogram (Kg)

Temperature Temperature is a measure of heat transfer Temperature Scales Celsius (°C) What is freezing point of water? What is boiling point of water? If it is 37 °C outside should you wear a sweater or a T-shirt? Kelvin (K ) SI unit A Kelvin is same size as a Celsius degree Location of 0 is different

Temperature measurements

Conversion between Celsius and Kelvin °C = K – 273 or K = °C + 273 Absolute Zero = 0 K What is this temperature in Celsius? -273°C Convert 25°C to K 298 K

How would you record the length of the nail?

Quantitative measurements Numerical quantity Appropriate unit Uncertainty of the measurement

How would you record these volumes?

How would you record this volume?

Uncertainty in measurement There is always some degree of uncertainty in any measurement Why? Measuring tool may have flaws Always some estimation involved when taking a measurement

An object of ~54g is placed on three different balances

                                                                                                                                                          All measurements have certain digits and one uncertain (estimated) digit

Significant Digits Measured digits in any measurement Includes all certain digits and one estimated digit Gives an indication of the accuracy of the instrument used for the measurement Examples: 3.54 cm 2 certain digits (3, 5) 1 uncertain digit (4) 3 significant digits 3.54 cm + 0.01cm

Atlantic-Pacific Rules Easy way to determine the number of significant digits in a measurement. Pretend your measurement is the US

Atlantic The decimal point is absent in the number Atlantic – Absent Start counting digits from atlantic side of the number. Start counting at your 1st non-zero number Example: 34500 3 sig dig

Pacific The decimal point is present in the number Pacific – Present Start counting digits from pacific side of the number. Start counting at your 1st non-zero number Example: 3.4500 5 sig dig

How many significant digits? 2.640 X 10-3 cm 287.0400Kg 6002 543 cars

Significant Digits in Calculations Calculated value cannot reflect a greater accuracy than the initial measurements Example: I travel 59 miles in 3 hours. What is my speed? 59miles/3hrs = 19.666666666667miles/hr 59miles/3hrs= 20miles/hr

Rounding 1. Determine the last sig dig your answer should have then round to that sig dig. Count from the left when determining last sig dig. Look at the number immediately to the right of the last sig dig. If it is less than 5 it is dropped. If it is 5 or greater increase the last sig dig by one. Examples 314.721m (4sig dig)  314.7m 0.001775m (2 sig dig)  0.0018m 8792m (2 sig dig)  8800m

Addition/Subtraction Answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places 30.962 g 264 g + 1.3 g 296.262  296g

Multiplication/Division Round the answer to the same number of significant digits as the measurement with the least number of significant digits (32.640m)(4.5 m) = 146.88m2  150m2

Practice 3419g + 3.912g + 7.0518g + 0.00013g = 145.63ml – 28.9ml = 20.8dm ÷123.1dm = 5.0cm x 5cm = (3.68 x 106m)(1.64 x 10-8m) = 1.22 x 10-9m

Precision Accuracy Reproducibility Standard deviation is measure or precision Correctness Percent error is measure of accuracy

Three groups of students measured the mass of a paper clip which had a known mass of 1.0004g. Average 2.601267 g 10.13255 g Which of the above sets of measurements are accurate Which are precise Which are precise and accurate Which are neither precise nor accurate

% Error Error = accepted value – experimental value % error = accepted value – experimental value x 100 accepted value

Example A lab technician experimentally determined the boiling point of octane to be 124.1C. The actual boiling point of octane is 125.7C. Calculate the % error. 125.7ºC – 124.1ºC x 100 = 1.3% 125.7ºC

Density Ratio of the mass of an object to its volume Density = mass g/ml or g/cm3 volume Density is an intensive physical property that depends only on the composition of the substance,not on the size of the sample The density of a substance usually decreasesas its temperature increases