42510011 0010 1010 1101 0001 0100 1011

Significant Figures and Scientific Notations

Examples and Problems

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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

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Significant figures: Rules for zerosLeading zeros are not significant.

Captive zeros are significant.

Trailing zeros are significant.

Leading zeroLeading zero

Captive zeroCaptive zero

Trailing zeroTrailing zero

0.421

4012

114.20

– three significant figures

– four significant figures

– five significant figures

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Significant Figures• Counting Sig Figs

–Count all numbers EXCEPT:

• Leading zeros -- 0.0025

• Trailing zeros without a decimal point -- 2,500

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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

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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

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Significant Figures• Calculating with Sig Figs (con’t)

– Exact Numbers do not limit the # of sig figs in the answer.• Counting numbers: 12 students

• Exact conversions: 1 m = 100 cm

• “1” in any conversion: 1 in = 2.54 cm

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Significant Figures

1. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

2. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

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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

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Scientific Notation

3. 2,400,000 g

4. 0.00256 kg

5. 7 10-5 km

6. 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

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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:

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