Observing, Measuring, & Calculating Chapter 1

Scientific Method https://www.brainpop.com/science/scientif icinquiry/scientificmethod/ Problem/Question – Observe a problem and ask a question. Research - Conduct background research. Write down your sources so you can cite your references. Hypothesis - Propose a hypothesis. This is an educated guess about what you expect.

Scientific Method cont. Experiment - Design and perform an experiment to test your hypothesis. Data/Analysis - Record observations and analyze what the data means. Often, you'll prepare a table or graph of the data. Conclusion - Conclude whether to accept or reject your hypothesis. Communicate your results.

Observing Matter *Qualitative observation – observation made without measurement *Quantitative observation – observation made through measurement

Measuring Matter *Measurement is used to quantify matter *Must be accurate (correct) *Must be precise (repeatable) Neither accurate nor precise Precise, but not accurate Precise AND accurate

Measuring Matter, cont. Accurate measurements *Rule: Measure what you know “for sure” plus one estimated digit *2 cm? 2.4 cm? 2.45 cm? *More significant digits = more accuracy 1 2

Measuring Matter, cont. *The accuracy of your measuring device determines the accuracy of your measurement *How accurate can the above measurement be? 1 2 3

Which is the most accurate measurement?

Significant Figures (Sig Figs) Used to determine the accuracy of a measurement or calculation Standard across all scientific disciplines More sig figs = more accurate

Counting Sig Figs – 6 Rules 1. All nonzero digits are significant 425 (3) 24.8 (3) 3.245 (4)

Counting Sig Figs – 6 Rules 2. Zeros between nonzero digits are significant 4052 (4) 3.05 (3) 4.001 (4)

Counting Sig Figs – 6 Rules 3. Zeros in front of nonzero digits are NOT significant 0.000342 (3) 0.01502 (4)

Counting Sig Figs – 6 Rules 4. Zeros on the end AND to the right of the decimal are significant 45.00 (4) 3.0 (2) 0.005200 (4)

Counting Sig Figs – 6 Rules 5. Zeros at the end and to the LEFT of the decimal are NOT significant 5000 (1) 4250 (3) 200 (1) **Use scientific notation to show sig figs with these kinds of numbers**

Scientific notation *Writes numbers in terms of powers of 10 4.5 X 10-3  0.0045 3.84 X 105  384,000 0.0098 9.8 X 10-3 25,000  2.5 X 104

Sig Figs, cont. 6. Unlimited sig figs A. Counted objects B. Defined quantities

How many sig figs? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs These all come from some measurements 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mL  2 sig figs This is a counted value 5 dogs  unlimited

Calculations and sig figs In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Ever heard that a chain is only as strong as the weakest link? Sometimes, calculated values need to be rounded off.

Rounding calculations Decide how many significant figures are needed (more on this very soon) Round to that many digits, counting from the left Is the next digit less than 5? Drop it. Next digit 5 or greater? Increase by 1

Rounding calculations, cont. 1. Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem ex/ 6.8 + 11.934 = 18.734  18.7 (3 sig figs)

Practice… Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL *Note the zero that has been added.

Rounding calculations, cont. 2. Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem. ex/ 6.38 x 2.0 = 12.76  13 (2 sig figs)

Practice… Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL

The Metric System System of base units and prefixes Based on powers of 10 Base units Length – meter (m) Mass – gram (g) Volume – liter (l) *note 1 cm3= 1ml water

Prefixes Mega M 106 Kilo k 103 Base unit 100 Deci d 10-1 Centi c 10-2 Milli m 10-3 Micro  10-6 Nano n 10-9 Pico p 10-12 Move decimal to right Move decimal to left

Metric conversions Convert 560 mL to L Convert 4.25 km to mm Convert 2,200 nm to m Convert 0.023 Mg to pg

Dimensional Analysis *A method of problem-solving using conversion factors Conversion Factor *Is essentially an equality ex/ 12 inches = 1 foot *Is written as a ratio to cancel units 12 inches OR 1 foot 1 foot 12 inches

Dimensional Analysis Problems 1. Convert 15 feet to inches. 2. Convert 176 feet to yards.

Dimensional Analysis, cont. 1. Convert 2,500 inches to yards. 2. Convert 0.0034 miles to inches.

Velocity V =

Suppose a polar bear were running on land chasing a snow rabbit Suppose a polar bear were running on land chasing a snow rabbit. If the polar bear runs at a speed of about 8.30 m/s, how far will it travel in 10.0 hours?

The longest stretch of straight railroad tracks lies across the desolate Nullarbor Plain, between the Australian cities of Adelaide and Perth. The tracks extend a distance of 478 km without a curve. How long would it take a train moving at a constant speed of 97.0 km/h to travel this length of track?