Significant Figures Factor Name Symbol Factor Name Symbol 10 -1 decimeter dm 10 1 decameter dam 10 -2 centimeter cm 10 2 hectometer hm 10 -3 millimeter

Significant Figures

Factor Name Symbol Factor Name Symbol

10-1 decimeter dm 101 decameter dam

10-2 centimeter cm 102 hectometer hm

10-3 millimeter mm 103 kilometer km

10-6 micrometer m 106 megameter Mm

10-9 nanometer nm 109 gigameter Gm

10-12 picometer pm 1012 terameter Tm

10-15 femtometer fm 1015 petameter Pm

10-18 attometer am 1018 exameter Em

10-21 zeptometer zm 1021 zettameter Zm

10-24 yoctometer ym 1024 yottameter Ym

Scientific Notation: Powers of Ten

Rules for writing numbers in scientific notation:

Write all significant figures but only the significant figures.

Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10o = 1

Examples: 3400 = 3.40 x 103 0.0120 = 1.20 x 10-2

Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!

Accuracy vs. Precision

Random errors: reduce precision

Good accuracyGood precision

Poor accuracyGood precision

Poor accuracyPoor precision

Systematic errors: reduce accuracy

(person)(instrument)

Precision Accuracy

reproducibility

check by repeating measurements

poor precision results from poor technique

correctness

check by using a different method

poor accuracy results from procedural or equipment flaws.

Reporting Measurements

• Using significant figures

• Report what is known with certainty

• Add ONE digit of uncertainty (estimation)

Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Practice Measuring

4.5 cm

4.54 cm

3.0 cm

Timberlake, Chemistry 7th Edition, page 7

cm0 1 2 3 4 5

cm0 1 2 3 4 5

cm0 1 2 3 4 5

Implied Range of Uncertainty

5 643

Implied range of uncertainty in a measurement reported as 5 cm.

5 643

Implied range of uncertainty in a measurement reported as 5.0 cm.

Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

5 643

Implied range of uncertainty in a measurement reported as 5.00 cm.

20

10

?

15 mL ?15.0 mL1.50 x 101 mL

Significant Figures

Indicate precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.35 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures

Counting Sig Figs

Count all numbers EXCEPT:

Leading zeros -- 0.0025

Trailing zeros without a decimal point -- 2,500


4. 0.080

3. 5,280

2. 402

1. 23.50

Significant Figures

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs


Significant Figures

Calculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF


Significant Figures

Calculating with Sig Figs (con’t)

Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures

Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm


Significant Figures

(15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF


Scientific Notation

Converting into scientific notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig. figs.

65,000 kg 6.5 × 104 kg


Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mmCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Scientific Notation

Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:


Proportions

Direct Proportion

Inverse Proportion

xy

xy

1

y

x

y

xCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

2. Zeros: There are three classes of zeroes.

a. Leading zeroes precede all the nonzero digits and DO NOT count assignificant figures. Example: 0.0025 has ____ significant figures.

b. Captive zeroes are zeroes between nonzero numbers. These alwayscount as significant figures. Example: 1.008 has ____ significant figures.

c. Trailing zeroes are zeroes at the right end of the number.

Trailing zeroes are only significant if the number contains a decimal point.Example: 1.00 x 102 has ____ significant figures.

Trailing zeroes are not significant if the number does not contain a decimalpoint. Example: 100 has ____ significant figure.

3. Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation.

2

4

3

1

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53

Documents

Significant Figures Factor Name Symbol Factor Name Symbol 10 -1 decimeter dm 10 1 decameter dam 10 -2 centimeter cm 10 2 hectometer hm 10 -3 millimeter