Unit 0:Observation,Measurementand Calculations : Unit 0:Observation,Measurementand Calculations Cartoon courtesy of NearingZero.net
Steps in the Scientific Method : Steps in the Scientific Method 1. Observations
- quantitative
- qualitative
2. Formulating hypotheses
- possible explanation for the observation
3. Performing experiments
- gathering new information to decide
whether the hypothesis is valid
Outcomes Over the Long-Term : Outcomes Over the Long-Term Theory (Model)
- A set of tested hypotheses that give an
overall explanation of some natural phenomenon.
Natural Law
- The same observation applies to many
different systems
- Example - Law of Conservation of Mass
Law vs. Theory : Law vs. Theory A law summarizes what happens
A theory (model) is an attempt to explain why it happens.
Slide 5 : In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron =
0.000000000000000000000000000000091 kg Scientific Notation
Slide 6 : Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg
x 602000000000000000000000 ???????????????????????????????????
Slide 7 : Scientific Notation: A method of representing very large or very small numbers in the form:
M x 10n M is a number between 1 and 10
n is an integer
Slide 8 : 2 500 000 000 Step #1: Insert an understood decimal point . Step #2: Decide where the decimal must end
up so that one number is to its left Step #3: Count how many places you bounce
the decimal point 1 2 3 4 5 6 7 8 9 Step #4: Re-write in the form M x 10n
Slide 9 : 2.5 x 109 The exponent is the number of places we moved the decimal.
Slide 10 : 0.0000579 Step #2: Decide where the decimal must end
up so that one number is to its left Step #3: Count how many places you bounce
the decimal point Step #4: Re-write in the form M x 10n 1 2 3 4 5
Slide 11 : 5.79 x 10-5 The exponent is negative because the number we started with was less than 1.
Slide 12 : PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION
Slide 13 : Review: Scientific notation expresses a number in the form: M x 10n 1 M 10 n is an integer
Slide 14 : 4 x 106 + 3 x 106 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 7 x 106
Slide 15 : 4 x 106 - 3 x 106 The same holds true for subtraction in scientific notation. 1 x 106
Slide 16 : 4 x 106 + 3 x 105 If the exponents are NOT the same, we must move a decimal to make them the same.
Slide 17 : 4.00 x 106 + 3.00 x 105 + .30 x 106 4.30 x 106 Move the decimal on the smaller number! 4.00 x 106
Slide 18 : A Problem for you… 2.37 x 10-6 + 3.48 x 10-4
Slide 19 : 2.37 x 10-6 + 3.48 x 10-4 Solution… 002.37 x 10-6
Slide 20 : + 3.48 x 10-4 Solution… 0.0237 x 10-4 3.5037 x 10-4
Nature of Measurement : Nature of Measurement Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x 10-34 Joule seconds Measurement - quantitative observation
consisting of 2 parts
The Fundamental SI Units (le Système International, SI) : The Fundamental SI Units (le Système International, SI)
SI Units : SI Units
SI PrefixesCommon to Chemistry : SI PrefixesCommon to Chemistry
Uncertainty in Measurement : Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Why Is there Uncertainty? : Why Is there Uncertainty? Measurements are performed with instruments
No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?
Precision and Accuracy : Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value.
Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate
Types of Error : Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low.
Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.
Rules for Counting Significant Figures - Details : Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.
3456 has
4 sig figs.
Rules for Counting Significant Figures - Details : Rules for Counting Significant Figures - Details Zeros
- Leading zeros do not count as
significant figures.
0.0486 has
3 sig figs.
Rules for Counting Significant Figures - Details : Rules for Counting Significant Figures - Details Zeros
- Captive zeros always count as
significant figures.
16.07 has
4 sig figs.
Rules for Counting Significant Figures - Details : Rules for Counting Significant Figures - Details Zeros
Trailing zeros are significant only if the number contains a decimal point.
9.300 has
4 sig figs.
Rules for Counting Significant Figures - Details : Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.
1 inch = 2.54 cm, exactly
Sig Fig Practice #1 : Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 2 sig figs
Rules for Significant Figures in Mathematical Operations : Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =
12.76 13 (2 sig figs)
Sig Fig Practice #2 : Sig Fig Practice #2 3.24 m x 7.0 m Calculation Calculator says: Answer 22.68 m2 23 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 ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL
Rules for Significant Figures in Mathematical Operations : Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.
6.8 + 11.934 =
18.734 18.7 (3 sig figs)
Sig Fig Practice #3 : Sig Fig Practice #3 3.24 m + 7.0 m Calculation Calculator says: Answer 10.24 m 10.2 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