significant figures and scientific notations examples and problems
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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.
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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
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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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
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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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
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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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
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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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
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
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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:
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem