Using Measurements

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# Using Measurements - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Using Measurements' - isaac-cox

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Presentation Transcript
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

accepted value

Percent Error
• Indicates accuracy of a measurement

% 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
• 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 Figures
• Counting Sig Figs(Table 2-5, p.39)
• Count all numbers EXCEPT:
• Trailing zeros without a decimal point -- 2,500
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

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
• 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 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
(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
• 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

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

Calculating with Scientific Notation

• 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

Calculating with Scientific Notation

• 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

Calculating with Scientific Notation

• Multiplication
• Digit terms are multiplied
• 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

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

y

y

x

x

Proportions
• Direct Proportion
• Inverse Proportion