Using Scientific Measurements 2.3

Objective/Warm-Up SWBAT identify and calculate significant figures and use scientific notation. What is the correct measurement for this buret? 4.85 mL

Notes-Accuracy Word/Phrase: Definition: Hints or diagram: Meaning in My own words: How close the measurement is to the real, true, or correct value accuracy

Notes-Precision Word/Phrase: Definition: Hints or diagram: Meaning in My own words: precision How close measurements are to each other

Add your own What would a picture look like that is neither precise nor accurate?

Percent Error Always some error in a measurement Instrument, limits of measurer, calibrations % error – calculated by the following formula… % error = Valueexp – Valueacc x 100 Valueacc

Objective/Warm-Up SWBAT review dimensional analysis, density, and metric conversions. Record the measurement for each cylinder.

Significant Figures Sig figs – all the digits known with certainty plus one final digit, which is somewhat estimated or uncertain Graduated cylinder example 42.5 mL - the 5 is the estimated number

Rules for Determining Sig. Figs. All non zero digits are significant Zeros at the end only count if there is a decimal point Decimal = go to 1st non zero and count everything to the right Exact numbers have infinite significant figures (1m = 1000mm) Calculators exaggerate precision

Sig. Fig Examples How many sig figs are in… 203000 1000.00 0.00052 0.06400 79.810

Significant Digits 4 4 4 3 4 3 4 2 3 4 3 2 2 5 1 Number # of Sig Figs 54.52 cm3 0.157 kg 0.106 cm 0.1209 m 28.0 mL 0.0067 g 2.690 g 2500 m 0.0230 cm3 43.07 cm 0.070 g 26.509 cm 1000 m 4 4 4 3 4 3 4 2 3 4 3 2 2 5 1

Objective/Warm-Up How many significant figures in these numbers? SWBAT review conversions and SI units. What is the measurement shown in the graduated cylinder? How many significant figures in these numbers? 5.0070 3.4000 3500 0.00120 0.07070

Objective/Warm-Up SWBAT accurately and precisely measure volume and calculate using scientific notation. How many sig figs are in… 203000 1000.00 0.00052 0.06400 79.810

Significant Figures Multiplication and division sig. figs = answer has no more figs. than the msmt. with the least # of sig. figs. 12.257 5 #’s x 1.162 4 #’s 14.2426340 4 #’s = 14.24

Multiply/Divide with Sig Figs Your answer must have the same number of sig figs as the measurement with the fewest number of sig figs. Calculate the volume if L = 3.65 cm, W = 3.20 cm, and H = 2.05 cm V = 23.944 cm3, after rounding to the correct number of sig figs, V=23.9 cm3

Significant Figures Addition and subtraction = answer has no more numbers to the right of the decimal pt. than the number with the least numbers to the right of the decimal. 3.9 5 2.8 79 + 213.6 220.4 29 = 220.4

Addition/Subtraction with Sig Figs Your answer must have the same number of decimal places as the value with the fewest decimal places 28.0 + 23.538 + 25.68 = 77.218 Round so that the answer is 77.2

Check-Up How can we judge accuracy? How can we judge precision? How do accuracy and precision relate to measurement?

Objective/Warm-Up Students will be able to use significant digits and scientific notation in calculations. Warm-Up: Section Review Worksheet

Scientific Notation 29640000000000000000000 copper atoms in 1 penny 2.964 x 1022 atoms 2 Parts to scientific notation # between 1 and 10 Power of 10

Scientific Notation We use the idea of exponents to make it easier to work with large and small numbers. 10,000 = 1 X 104 250,000 = 2.5 X 105 Count places to the left until there is one number to the left of the decimal point. 230,000 = ? 35,000 = ?

Scientific Notation Continued 0.00006 = 6 X 10-5 0.00045 = 4.5 X 10-4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? 0.0000025 = ?

Scientific Notation Examples Change from scientific notation the distance from Pluto to the Sun is 5.9×10 12 meters the Milky Way disk radius is 3.9×1020 meters. The speed of light is 3 x 10 8 meters/second. the sun is 1.5x 1011 meters from earth Mass of proton : 1.6726 x 10-27 kg Mass of neutron: 1.6749 x 10-27 kg Mass of electron: 9.10939 × 10-31 kg Change into scientific notation 0.000 000 000 753 kg is the mass of a dust particle A proton has a diameter of approximately 0.000000000001 mm

Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000

Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01 10-3 = 1/1000 = 0.001 10-4 = 1/10000 = 0.0001

Quick Review When multiplying: When dividing: Add the exponents Subtract the exponents

Multiplying with Scientific Notation Add the Exponents 102 X 103 = 105 100 X 1000 = 100,000

Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 X 103 = 105 7.59 X 105, round to 7.6 x 105

Multiplying with Scientific Notation (4.6 X 104) X (5.5 X 103) = ? (3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation Subtract the Exponents 104/103 = 101 10000/ 1000 = 10

Dividing with Scientific Notation (3.3 X 104)/ (2.3 X 102) 33000 / 230 = 143.4783 Divide the Coefficients 3.3/ 2.3 = 1.434783 Subtract the Exponents 104 / 102 = 102 1.4347823 X 102, round to 1.4 x 102

Dividing with Scientific Notation (4.6 X 104) / (5.5 X 103) = ? (3.1 X 103) / (4.2 X 105) = ?

Wrap-Up Summarize the rules for multiplying and dividing in scientific notation. Why do we use scientific notation?

Scientific Notation 0.000000000000003332 kg 3.332 x 10-15 kg 1970000000 L 1.97 x 109 What is ….. In scientific notation? 4.58 x 105 9.05 x 10-3