The Fundamental Tools Of Science

Units Some fundamental measurements in all of science: Length Time Mass Many others are combinations of these: Energy, Speed, Volume, Area *THINK: What does it mean to be a combined unit?

Units International Standard Units (SI, aka metric) Length (m – meter) Mass (kg – kilogram) Time (s – seconds) Energy (J – joules) Temperature (K – kelvin)

Temperature Scales Fahrenheit Celsius Kelvin 32 ˚F 212 ˚F 180˚F 100 ˚C Boiling point of water 32 ˚F 212 ˚F 180˚F 100 ˚C 0 ˚C 100˚C 373 K 273 K 100 K Freezing point of water Notice that 1 kelvin degree = 1 degree Celsius

Temperature Scales 100 oF 38 oC 311 K oF oC K

Significant Figures: Digits in a measurement having values that are known with certainty plus one digit having a value that is estimated.

Reading Volume: Significant Figures on an Instrument Record the digits you know for sure, then estimate one place. What do you get for these two measurements?

Measurements that contain a greater number of significant figures are more precise than measurements that contain fewer significant figures. Always select an instrument that gives you the most significant figures. Only report as many sig figs as that instrument allows

The Rules ATLANTIC PACIFIC

All numbers 1-9 are significant. Zeros are sometimes significant, here's how you can tell: If a decimal point is present, starts on the Pacific side, move across until you get to a 1-9 digit, and start counting to the end If a decimal point is absent, start on the Atlantic side, move across until you get to a 1-9 digit, and start counting to the end 1.100 has ? sig figs, 0.00540 has ?, 40.01 has ? 1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ?

When multiplying or dividing measurements: round the answer to the same number of digits as the measurement having the fewest number of significant figures. When adding or subtracting measurements: round the answer to the place value of the measurement with the least significant place value.

123456.7890 Identify the LEAST PRECISE measurement. Higher precision 123456.7890 Lower precision Identify the LEAST PRECISE measurement. Identify the MOST PRECISE digit (place) within that measurement. Round the answer to this digit (place).

Conversion Commonly Used Prefixes: kilo = 1000 of something ( 1km= 1000m, kg) deci =0.1 of something (10 dm = 1m) centi = 0.01 of something (100 cm = 1m) milli = 0.001 of something (103 mm = 1m) micro = 0.000001 (106 µm = 1m) nano = 0.000000001 (109 nm = 1m) pico = 0.000000000001 (1012 pm = 1m) Refer to Conversion Chart to additional prefixes

Conversion = = 1 = = 1 All conversion factors are fractions. = 100 cm 100 cm 1 m 100 cm = = 1 The top and bottom of a conversion factor must equal each other. 1 km 103 m 103 m = 1 = Therefore, every conversion factor must equal 1. 1m 10-6 µm 10-6 µm = = 1 When you multiply a measurement by 1 you do not change its value!

How many seconds are in 54 days? Write the measurement with its unit. If it isn’t already a fraction, write it over 1. Set up conversion factors that Cancel units you want to get rid of Replace with units you are looking for Have values on the top and bottom that are equivalent Multiply numbers across the top Multiply numbers across the bottom Divide to get answer, check units

54 days . 24 hours . 60 mins . 60 secs = 1 1 day 1 hour 1 min This is how you set up the conversions for the problem on the previous slide: 54 days . 24 hours . 60 mins . 60 secs = 1 1 day 1 hour 1 min To solve, check that units cancel and leave you with the unit you want. Then, multiply across the top, multiply across the bottom, then divide your answers.

Try a few more… 2 m = ____ cm 34.5 mm = ____ m 24 in = _____ m (Hint: sometimes we need more than one conversion factor!) OH WOW THIS LOOKS HARD!!! 15.0 miles = _______ ft hour sec Conversions you don’t need to memorize: 5280 ft = 1 miles 3 feet = 1 yard 12 in = 1 ft 2.54 cm = 1 in (Hint: units on the bottom can be changed, too! Also, per hour means 1 hour and per sec means 1 sec….)

The Nature of Units Units are multiplied and divided like numbers are. 10 meters 2 meters = 5 (the units cancel out) 10 meters x 10 meters x 10 meters = 103 m3 (the units combine as exponents) 50 miles 10 gallons = 5 miles/gallon (the units combine as a fraction) Only IDENTICAL UNITS on 2 numbers can be added or subtracted. The answer always has the same units. 100 kg – 25 kg = 75 kg 100 kg – 25 m = Meaningless Dribble

Scientific Notation 10000000000000000000000 0.00000000000000000000000000001 There has to be a better way to write those numbers Rules for scientific notation 1) Always express the number starting with the one’s place followed by any decimal digits, times a power of 10. 2)To express a large number, count the number of decimal places needed to move to the one’splace, and make that number the exponent of ten. 3) To express a very small number, count the number of decimal places needed to move to the one’s place, and make that number the NEGATIVE exponent of ten. 4) After re-expressing the number in scientific notation, check it by writing out the expanded ten, and multiply it by the measured number.

Scientific Notation Examples: 0.0000000000000000000000000000000010 94140000000000000000000000000000000 = 9.414 x 1035 Scientific notation is a great way to display significant digits: The significant digits appear before the x10 in Scientific Notation!

More About Unit Conversions Sometimes we need to convert squared or cubed units…. IT’s EASY! Just square or cube the conversion factor. Convert 0.62 m2 to cm2 = 6200 cm2

Accuracy Precision What's the difference??

Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise

Instruments are... Precise if they give many significant digits Accurate if calibrated to a standard

Observed – True X 100 True Percent Error To report the accuracy of your measurements Observed – True True X 100

To report the precision of your measurements Average Deviation To report the precision of your measurements 1 Average your measurements 2 Find the absolute values of the differences between each measurement and the average 3 Average these differences