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Measurements and Calculations. Using Measurements. Accuracy vs. Precision. Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other. ACCURATE = CORRECT PRECISE = CONSISTENT. your value. accepted value. Percent Error.

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accuracy vs precision
Accuracy vs. Precision
  • Accuracy- how close a measurement is to the accepted value
  • Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

percent error

your value

accepted value

Percent Error
  • Indicates accuracy of a measurement
percent error1

% error = 2.9 %

Percent Error
  • A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
significant figures
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

significant figures1
Significant Figures
  • Counting Sig Figs(Table 2-5, p.39)
    • Count all numbers EXCEPT:
      • Leading zeros -- 0.0025
      • Trailing zeros without a decimal point -- 2,500
significant figures2
Significant Figures

Counting Sig Fig Examples

1. 23.50

1. 23.50

4 sig figs

3 sig figs

2. 402

2. 402

3. 5,280

3. 5,280

3 sig figs

2 sig figs

4. 0.080

4. 0.080

significant figures3

3 SF

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

4 SF

3 SF

324g

c significant figures
C. 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.

224 g

+ 130 g

354 g

224 g

+ 130 g

354 g

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL

 350 g

 7.9 mL

c significant figures1
C. 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
significant figures4
(15.30 g) ÷ (6.4 mL)

 2.4 g/mL

2 SF

Significant Figures

Practice Problems

4 SF

2 SF

= 2.390625 g/mL

18.9 g

- 0.84 g

 18.1 g

18.06 g

scientific notation
Scientific Notation
  • Converting into Sci. 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 notation1
1. 2,400,000 g

2. 0.00256 kg

3. 7  10-5 km

4. 6.2  104 mm

Scientific Notation

Practice Problems

2.4  106 g

2.56  10-3 kg

0.00007 km

62,000 mm

slide14

Calculating with Scientific Notation

  • Addition and Subtraction
  • All numbers are converted to the same power of 10
  • Digit terms are added or subtracted
  • Example:
  • (4.215 x 10-2 g) + (3.2 x 10-4 g) =
  • (4.215 x 10-2 g) + (0.032 x 10-2 g) = 4.247 x 10-2 g
  • = 4.247 x 10-2 g
  • Answer must be rounded correctly

DON’T forget the UNITS

slide15

Calculating with Scientific Notation

  • Addition and Subtraction
  • All numbers are converted to the same power of 10
  • Digit terms are added or subtracted
  • Example:
  • (8.97 x 104g) - (2.62 x 103 g) =
  • (8.97 x 104 g) - (0.262 x 104 g) = 8.708 x 104 g
  • = 8.71 x 104 g
  • Answer must be rounded correctly

DON’T forget the UNITS

slide16

Calculating with Scientific Notation

  • Multiplication
  • Digit terms are multiplied
  • Exponents are added
  • Example:
  • (3.4 x 106 cm)(4.2 x 103 cm) =
  • (3.4 cm)(4.2 cm) x 10(6+3) = 14.28 x 109 cm2
  • = 1.4 x 1010 cm2
  • Answer must be rounded correctly

DON’T forget the UNITS

slide17

Calculating with Scientific Notation

  • Multiplication
  • Digit terms are divided
  • Exponents are subtracted
  • Example:
  • (3.2 x 103 g)/(5.7 x 10-2 g/mol) =
  • (3.2 g)/(5.7 g/mol) x 10(3-(-2)) = 0.561 x 105 mol
  • = 5.6 x 104 mol
  • Answer must be rounded correctly

DON’T forget the UNITS

proportions

y

y

x

x

Proportions
  • Direct Proportion
  • Inverse Proportion