Units, Metric System, Conversions, Uncertainty, Significant Figures, Scientific Notation &

Units, Metric System, Conversions, Uncertainty, Significant Figures, Scientific Notation & Dimensional Analysis And not necessarily in that order!

Warm Up • You read on the internet that a group identified as the Pleiadians and other cosmic Beings of Light use tachyons as their basic source of energy: as a hyper drive for their beam ships by creating hyperspace wormholes, for healing, information transmission and for other purposes. What further information would you need to know to decide whether or not this was in the realm of science of not.

What unit should you use? Luminous Intensity  candela

Temp  Kelvin 24 22

Mass  kilograms

20 18

Electricity  Ampere

16 14

Length  meters

12 10 8 6

Time  seconds

4

Amount of substance  mol

SI Units •

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•

•

•

•

•

Meter Standardized: 1983 Measures: Length Definition: The distance traveled by light in a vacuum in 1/299,792,458 second Second Standardized: 1967 Measures: Time Definition: The time it takes for a cesium-133 atom to cycle 9,192,631,770 times between two specific quantum states Ampere Standardized: 1948 Measures: Electrical current Definition: The current required to create a force of 2 x 10-7 newtons per meter between two parallel wires Kelvin Standardized: 1954 Measures: Temperature Definition: 1/273.16 the temperature of the triple point of water — when it's simultaneously gas, liquid, and solid Mole Standardized: 1971 Measures: Amount of stuff Definition: The number of atoms in 12 grams of carbon 12 (6.022 x 1023 ) Candela Standardized: 1979 Measures: Brightness Definition: The intensity of a 1/683-watt yellow-green light spread over a square meter, seen from a meter away Kilogram Standardized: 1889 Measures: Mass Definition: Standard based on a physical sample of platinum-iridium metal held at the International Bureau of Weights & Measures in Paris, France.

X X

AHHHH! This chocolate milk is killing me!

Metric Conversion Factors Prefix

Multiplied By

Symbol

Conversions to Know

Giga

109

G

Mega

106

M

Kilo

1000

k

1 gigabase = 1 x 109 base 1 megabase = 1 x 106 base 1 kilobase = 1 x 103 base

Hecto

100

h

Deka

10

da

Base unit: m, L, g, etc

1

m, L, g

Deci

0.1

d

Centi

0.01

c

Milli

0.001

m

Micro

10-6

µ or r

Nano

10-9

n

1 base = 100 centibase 1 base = 1000 millibase 1 base = 1 x 106 microbase 1 base = 1 x 109 nanobase

Scientific Notation - Why? It is easier to write Calculations are simplified Significant figures are clear

6.022x10

23

is so much easier to write than 602,200,000,000,000,000,000,000

Scientific Notation – How? Converting numbers to scientific notation Move the decimal point until there is only one digit 0.0034060  (a non-zero one) to the left of it. 3.4060 Keep track of the number of places you moved the three spaces; decimal, and write the number as a superscript over 3.4060 x 103 the number ten. If you moved the decimal to the right, the exponent was moved right; becomes negative; if to the left, then it remains 3.4060 x 10-3 positive. All significant figures from the original number must be kept in scientific notation!

five sig figs 3.4060 x 10-3

sdrawkcaB gnioG Converting from scientific notation to regular numbers Move the decimal point the number of 7.45 x 104  74,500 places left (if negative exponent) or right (if positive exponent) that is indicated in the power of ten. Add extra zeros for placeholders if necessary.

Vocabulary Accuracy: how close a measurement is to the known, accepted or correct value Example: A student measures the temperature of boiling water to be 100.0°C Precision: how close several measurements are to each other Example: Six different students measure the temperature of boiling water to be 98.2°C, 98.1°C, 98.0°C, 98.1°C, 98.3°C, 98.2°C.

Accurate or precise?

Precise but not accurate

Not accurate NOR precise

Accurate AND precise

Accurate (on average) but NOT precise

Striving for Accuracy & Precision For each of the following scenarios… 1. Discuss whether or not the resulting measurements will be precise. Why? 2. Discuss whether or not we can know if the measurements are accurate. Why? Scenario #1: An instrument is mis-calibrated, and one person uses it to take the same measurement multiple times. Scenario #2 Many people use the same correctly calibrated instrument to take the same measurement multiple times. Scenario #3 One person takes the same measurement multiple times but uses many different instruments of the same type.

Estimating • Precision can also refer to how well you can know a measured number or how many decimal places (sig. figs) you can give a measurement • Not all measuring devices have the same precision. Not all measurements will be whole numbers. It is important to be able to estimate and interpolate. • Look back at your warm up data, convert your marking measurements to centimeters • How much precision (how many digits) can you really claim to know?

Significant Figures Why aren’t all figures significant? Rules 1. All non-zero digits are always significant. All counting numbers are significant and have an infinite number of significant figures.

Examples

8.314 Latm/molK 22.4 L/mol 1842 Gunn students 2. Zeros between non-zeros are always significant. 2005 years $10.99 12.011 g/mol carbon 3. Zeros in front of non-zeros are not significant. 0.028 0.00001 09 September 4. Zeros at the end of a number and to the right of a decimal are 1.0000 mm significant. 2.80 years 5. Zeros at the end of a number and to the left of a decimal may or may not 2000 be significant. 2000 AD Hints: Zeros that are counted or measured are significant; 2000 gallons Zeros that hold places are not. 2.0x103 gallons Use scientific notation or a decimal point for clarity. 2000. gallons

Atlantic Pacific Rule a. Decimal present → count from the Pacific side Decimal absent → count from the Atlantic side b. Find the first non-zero digit c. All other digits are significant

Practice How many significant figures in each of the following numbers?

0.0026701 m

5

19.0550 kg

6

3500 V

2

1,809,000 L

4

0.86250 g

5

Warm Up! Warm Up: How many significant figures are in the following numbers ? 2.0051, 2099623002, 0.00203020400, 0.1 5000, 100,000.00000, 20409595000.0, 0.0000000000001

Measurement - Volume Always use a graduated cylinder Bring it to your eye level Read the bottom of the meniscus Report the smallest calibration plus one estimated digit

21.6 ml

Measurement Temperature

Mercury adheres better to itself than the glass, so the meniscus goes the other way. Read the top of the meniscus. Report the smallest calibration plus one estimated digit

24 22 20 18 16 14 12 10 8 6 4

Measurement - Mass On an electric balance, report all the digits, knowing that the last digit contains an estimate 0.042 g

Measurement - length Use a ruler with the finest markings practical for the application. Line the object up with the ‘0’. Report the smallest calibration plus one estimated digit

Math with Significant Figures Operation Addition or Subtraction

Rule

Example

Keep the number of significant figures to the 102kg + 1.2kg = 103.2kg  103kg least measured place value.

10.99m - 0.564m = 10.426m  _____

Multiplication or Keep the number of significant figures of the 102kg * 1.2kg = 122.4 kg2 120 kg2 or 1.2x102 kg2 Division number with the fewest digits.

Combination of operations.

10.99 ÷ 0.564 = 19.4858416  _____

Follow the rules for order of operations 0.185(1,627.3 + 450) – 8 = ?? (Please Excuse My Dear Aunt Sally) and keep 0.185(2077.3) – 8  0.185(2077)–8 track of the number of significant figures you 384.3005 – 8  384 – 8 would have at each step, but don’t round until 376.3005  376 the end. Remember counting numbers are infinitely 10(26.127*0.95 + 15.5*0.05) = ?? significant! (assume 10 is a counting number)

Appropriate Metric Units • For each of the following, assign appropriate units of metric measurement. Use any necessary prefixes. Length of a bus Mass of a dog Volume of your key chain & keys Width of the United States Mass of a pencil Volume of water in a lake Depth of a tissue box Mass of a grain of sand Volume of water in a tub Width of a wire

Dimensional Analysis Problem: How many seconds are in a year? •

Identify your starting and ending units. Know where you are starting from and where you are going to. Starting unit: year? ending unit: seconds ? 2. Write down your starting value on the left hand side of your work space, and your ending value on the right hand side. Always include units for everything! 1 year seconds

3. Identify any other information you may need. 1 year = 365.25 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds 4. Write down each conversion with the numerator (top value in the fraction) being the unit you want to be in, and your denominator (bottom value in the fraction) being the unit you want to get out of or cancel out.

 365.25days     1 year 

 24hours   60 min   60 sec         1day   1hour   1 min 

5. When finished, carefully inspect your work to ensure that all values are correct, have units, and that all units cancel out except for the last one which is the one you want to be in.  365.25days  24hours   60 min   60 sec  1 year      = ? sec  1 year  1day   1hour   1 min 

6. Finally, multiply all values across the top and divide by all values multiplied across the bottom. 7

3.1558 x 10 sec