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

Temperature Scales 100 o F 38 o C 311 K oFoF oCoCK

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 PACIFICPACIFIC ATLANTICATLANTIC

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 1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ? has ? has ? sig figs, 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.

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

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 = of something (10 3 mm = 1m) –micro = (10 6 µm = 1m) –nano = (10 9 nm = 1m) –pico = (10 12 pm = 1m) Refer to Conversion Chart to additional prefixes

All conversion factors are fractions. Conversion 100 cm 1 m 100 cm 1m µm == 1 = µm 1 km 10 3 m = = m The top and bottom of a conversion factor must equal each other. Therefore, every conversion factor must equal 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 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. This is how you set up the conversions for the problem on the previous slide:

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 (Hint: units on the bottom can be changed, too! Also, per hour means 1 hour and per sec means 1 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

Units are multiplied and divided like numbers are. The Nature of Units 10 meters 2 meters = 5 (the units cancel out) 50 miles 10 gallons = 5 miles/gallon (the units combine as a fraction) 10 meters x 10 meters x 10 meters = 10 3 m 3 (the units combine as exponents) 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 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: = 1.0 x = x 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 m 2 to cm 2 = 6200 cm 2

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

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

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

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