I

II

III

I. Using Measurements

CH. 2 - MEASUREMENT

A. 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

A. Accuracy vs. Precision

Precise

Accurate

Precise

Not Accurate

Not Precise

Not Accurate

B. Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

B. 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.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %

C. 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

C. Significant Figures

6.34 cm

C. Significant Figures

Rule 1- any # other than 0 is significant

Example 123.45 has 5 SF

C. Significant Figures

Rule 2- any 0’s between significant figures are significant

Example- 1002.05 has 6 SF1002 has 4 SF

C. Significant Figures

Rule 3- All final 0s after a decimal are significant

Example- 12.740 has 5 SF92100. has 6 SF

C. Significant Figures

Rule 4- )s used for spacing are not significant

Example- 921000 has 3 SF.00000233 has 3 SF

4. 0.080

3. 5,280

2. 402

1. 23.50

C. 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

C. Significant Figures

Rounding If the digit to be removed is:

< 5, round down > 5, round up = 5, round to the nearest even number

4. 78.5543 kg

3. 2.7851 cm

2. 17.32 m

1. 42.68 g

C. Significant Figures

Rounding ExamplesRound each number to 3 sig figs

42.7 g

17.3 m

2.78 cm

78.6 kg

C. 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

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.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.76 mL

+ 4.1 mL

7.86 mL

224 g

+ 130 g

354 g

C. 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

C. Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

D. 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

D. 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 mm

D. Scientific Notation

Calculating with Sci. 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: