Using Scientific Measurements 2.3 Objective/Warm-Up SWBAT identify and calculate significant figures...

Using Scientific Measurements

2.3

Objective/Warm-Up

• SWBAT identify and calculate significant figures and use scientific notation.

• What is the correctmeasurement forthis buret?

4.85 mL

Notes-Accuracy

Word/Phrase: Definition:

Hints or diagram: Meaning in My own words:

accuracy How close the measurement is to the real, true, orcorrect value

Notes-Precision

Word/Phrase: Definition:

Hints or diagram: Meaning in My own words:

precision How close measurementsare to each other

Add your own

• What would a picture look like that is neither precise nor accurate?

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 DigitsNumber # of

Sig Figs

Number # of Sig Figs

Number # of Sig Figs

6.751 g 30.07 g 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

3

3

2

2

4

3

2

3

5

4

4

4

4

1

Objective/Warm-Up• 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 #’sx 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 cmV = 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 places28.0 + 23.538 + 25.68 = 77.218Round 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 notation1. # between 1 and 102. 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 ExamplesChange from scientific notationa) the distance from Pluto to the Sun is 5.9×10 12 metersb) the Milky Way disk radius is 3.9×1020 meters.c) The speed of light is 3 x 10 8 meters/second.d) the sun is 1.5x 1011 meters from earthe) Mass of proton : 1.6726 x 10-27 kgf) Mass of neutron: 1.6749 x 10-27 kgg) Mass of electron: 9.10939 × 10-31 kg Change into scientific notationh) 0.000 000 000 753 kg is the mass of a dust particlei) A proton has a diameter of approximately 0.000000000001 mm

Positive Exponents

• 101 = 10• 102 = 10X10= 100• 103 = 10X10X10 = 1000• 104 = 10X10X10X10 = 10,000

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:– Add the exponents

• When dividing:– 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