Numbers & Measurement The Importance of Units � Measurement quantifies an observation. � It consists of 2 parts and relates to the instrument (tool) used for the measurement. Part 1 - numberPart 1 - number Part 2 - unitPart 2 - unit [NOTE: There is UNCERTAINTY in every observation (measurement) and the resulting number.] [NOTE: There is UNCERTAINTY in every observation (measurement) and the resulting number.]

Numbers & Measurement The Importance of Units & Writing Numbers Correctly � Examples: ,000135,   1.12    1.20   1.20    � Examples: 15.0 grams of fat15.0 grams of fat 135 Calories in 15.0 g135 Calories in 15.0 g 135 kcal in 15.0 g135 kcal in 15.0 g 135,000 cal in 15.0 g135,000 cal in 15.0 g 1.80 Liters (~ 1/2 gal:the volume of water that can be boiled.)1.80 Liters (~ 1/2 gal:the volume of water that can be boiled.) 1.12    molecules1.12    molecules 1.20    cal/ molecule1.20    cal/ molecule UNCERTAINTY is in the last “significant”digit of the number. Leading or trailing zeroes present a challenge.

Measurements (Units) Only three countries currently use “English” units of measure. Can you name them? The United States, Liberia and Burundi.

English Metric Comparisons

Mass vs. Weight English vs. Metric

Numbers Correctly expressing a number is determined by the actual instrument (tool) used in the measurement! How many numbers should I include? Only those that are significant. “Significant Digits (Figures)” The number suggests the exactness of the measured value. © Copyright R.J. Rusay

What is the length of the rod? Different measurement tools give different numbers: Which ruler is better? ? cm cm cm

? mL Each line = 1 mL mL OK NOT mL

Volume of an object (any shape) by displacement What is the volume of the jade? 60.5 mL 60.5 mL mL 10.5 mL 10.5 mL

Mass Determination Weighing Devices: Balances (Scales)

Measurements: Scale Powers of Ten (Exponents: 10 x ) � Scale: Macroscopic (large) vs. Microscopic (small) � Comparisons in scale: � Units of ten vs. fractions � Using ten(s); language can describe wide ranges of scale (prefixes) � Relates to Scientific Notation (counting decimal places [tens])

Powers of Ten

Shorthand Prefixes

World’s smallest man-made image The above image is 7  m x 10  m. [ Nature, 412, 697 (2001) ] m x m  = micro (10 -6 = 1/ 1,000,000)

Commonly used prefixes Kilo-, centi-, milli- should be known from memory.

Conversion Factor Method (Dimensional Analysis) Qualitative Descriptions vs. Quantitative Use exact numbers / “scale factor” UNITS A Bookkeeping Method: Example ___ ft___in > ? m (1 ft = 12 in; 2.54 cm = 1 in; 100 cm = 1 m) ___ft x 12 in/ft + ___in = ___in ___in x 2.54 cm/in x 1 m/100cm = ___m © Copyright R.J. Rusay

Scientific Notation & Significant Digits Scientific Notation: A single digit followed by a decimal and a power of ten. Examples: 2,345 mL and g 2,345 mL = x 10 3 mL g = x g

What is the area of the world’s smallest man- made image in square inches? The above image is 7  m x 10  m. [ Nature, 412, 697 (2001) ]  = micro (10 -6 = 1/ 1,000,000) m x m A = l x w A = 7 x m 2

World’s fastest computer (12 TeraFLOPS/second) Cost? ~$ 30,000,000

When told to begin, count 1+1. Keep repeating counting 1+1 until you are told to stop, keep track of how many times that you have repeated 1+1. The median for our group is:______ (Average vs. Median?) There about 60 of us here. The estimated processing power for our group is:_______. This is equal to how many FLOPS (Floating Point OPerations/ sec.)?_____ How many people would be needed to produce 1 teraFLOP (I.e. adding 1+1)?_____ The estimated population of the world is 6.2 billion people. How many world populations are needed to do the work of a 12 teraFLOP computer?______ Floating Point Operations Flops

Measurements: Precision & Accuracy Which is most precise? I.e. the smallest average difference between the darts in each set. Which is the most accurate set? I.e. the average is closest to the target center. c > b > a c > b > a c > a > b c > a > b

Precision & Accuracy Numerical Data The accepted value is Rank the relative precision & accuracy of the three sets of data. Precision: b > c > a Accuracy: c > a = b