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Chapter 3Chapter 3Scientific Scientific

MeasurementMeasurement

MeasurementsMeasurements

QualitativeQualitative Gives results Gives results

in a in a description, description, nonumerical nonumerical

formform

QuantitativeQuantitative Give results in Give results in

a definite a definite form, usually form, usually numbers and numbers and unitsunits

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

Accuracy vs. Precision

Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

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 %

Percent Error

A technician experimentally determined the boiling point of octane to be 124.1ºC. The actual boiling point of octane is 125.7ºC. Calculate the error and percent error.

Error= 1.6ºC

Percent error= 1.273 %

Significant Figures

Indicates precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.31 cm

Significant Figures

Counting Sig Figs All non-zero numbers are sig figsAll non-zero numbers are sig figs Zeros depend on location in number:Zeros depend on location in number:

LEADING zeros LEADING zeros nevernever count --------- count ---------0.0025 EMBEDDED zeros EMBEDDED zeros alwaysalways count---- 10,005 count---- 10,005 TRAILING zeros TRAILING zeros onlyonly count if count if

there is a point. --------------there is a point. --------------2,500 2,500.

The underlined zeros do not count.

4. 0.080

3. 5,280

2. 402

1. 23.50

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

Rounding

Need to use rounding to write a calculation correctly

Calculator gives you lots of insignificant figures and you must round to the right place

When rounding, look at the digit after the one you can keepGreater than or equal to 5, round upLess than 5, keep the same

Round each measurement to 3 sig figs.

A. 87.073 meters B. 4.3621 meters C. 0.01552 meter D. 9009 meters E. 1.7777 meters F. 629.55 meters

Rounding

87.1meters

4.36 meters

0.0155 meter

9010 meters

1.78 meters

630 meters

Scientific Notation

Round each measurement to the number of significant figure shown in parenthesis. Write the answers in scientific notation.

A. 314.721 meters (4) B. 0.001775 meter (2) C. 64.32 X 10-1 meters (1) D. 8792 meters (2)

3.147 X 102

1.8 108

60 X 10-1

8.8 X 103

3.75 mL

+ 4.1 mL

7.85 mL

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 7.9 mL350g

224 g

+ 130 g

354 g

Significant Figures

C. 8.7 g + 15.43 g + 19 g = 43.13 g D. 853.2 L – 627.443 L = 225.757 L E. 5.47 m + 11m + 87.3000 m =

103.770m

C. 8.7

15.43

+ 19

43.13

D. 853.2

- 627.443

225.757

43 225.8

E. 5.47

11

+ 87.3000

103.770

104

Significant Figures

Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answer. UNLIMITED SIG FIGSCounting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

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

Significant Figures

1. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

3700a. 67 X 55 = 3685

4 SF 2 SF

2.4 g/mL2 SF

d. 0.034 X 8.8 = 0.2992 0.30

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 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

Scientific Notation

Convert between scientific notation and regular notation *without changing the # of sig figs*

A. 4.61 X 10-4

B. 3.69 X 106

C. 0.000597 D. 23,000,000 E. 8.00 X 102

Scientific Notation

Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

(5.44 X10 EEEE ÷÷ EEEE ENTERENTER7) (8.1X10 4)

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator: