Measurements and Calculations Chapter 2. Objectives Construct and use tables and graphs to interpret...

Measurements and Calculations

Chapter 2

Objectives

• Construct and use tables and graphs to interpret data sets.

• Solve simple algebraic expressions.• Measure with accuracy and precision (length,

volume, mass, temperature, time, etc.)• Convert within a unit (such as, centimeters to

meters).• Use common prefixes such as milli-, centi-, and

kilo-.• Use scientific notation, where appropriate.• Use ratio and proportion in the solution of

problems.

Objectives

•Determine the correct number of significant figures.•Determine percent error from experimental and accepted values.•Use appropriate metric/standard international (SI) units of measurement for mass (kg); length (m); and time (s).•Use Celsius and Kelvin scales.

Counting Significant Figures

1. All non-zero digits are significant– 1.5 has 2 sig. figs.

2. Interior zeros are significant– 1.05 has 3 sig. figs.

3. Leading zeros are NOT significant– 0.001050 has 4 sig. figs.

Presentation of Lecture Outlines, 1–4

Tro: Chemistry: A Molecular Approach, 2/e

Counting Significant Figures4. Trailing zeros may or may not be significant

a) Trailing zeros after a decimal point are significant

• 1.050 has 4 sig. figs.

b) Trailing zeros before a decimal point are significant if the decimal point is written

• 150.0 has 4 sig. figs.

c) Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation

• if 150 has 2 sig. figs. then 1.5 x 102

• but if 150 has 3 sig. figs. then 1.50 x 102



Significant Figures and Exact Numbers• A number whose value is known with complete

certainty is exact– from counting individual objects– from definitions

• 1 cm is exactly equal to 0.01 m

– from integer values in equations• in the equation for the radius of a circle, the 2 is exact


• Exact numbers have an unlimited number of significant figures


Example 1.5: Determining the Number of Significant Figures in a Number


How many significant figures are in each of the following?

0.04450 m

5.0003 km

10 dm = 1 m

1.000 × 105 s

0.00002 mm

10,000 m

4 sig. figs.; the digits 4 and 5, and the trailing 0

5 sig. figs.; the digits 5 and 3, and the interior 0’s

infinite number of sig. figs., exact numbers

4 sig. figs.; the digit 1, and the trailing 0’s

1 sig. figs.; the digit 2, not the leading 0’s

Ambiguous, generally assume 1 sig. fig.


Study Buddy Review: Identify S.F.

1. 523.1 mL

2. 0.0025 mg

3. 5002 km

4. 1.8 x 10 6 lbs.

5. 0.090180 L

6. 2000 dogs

7. 2010. cats

8. 14,000.00 carrots

Study Buddy Review: Identify S.F.

1. 523.1 mL 4

2. 0.0025 mg 2

3. 5002 km 4

4. 1.8 x 10 6 lbs. 2

5. 0.090180 L 5

6. 2000 dogs 1

7. 2010. cats 4

8. 14,000.00 carrots 7

Multiplication and Division with Significant Figures

• When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the lowest number of significant figures

5.02 × 89.665 × 0.10 = 45.0118 = 453 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs.

5.892 ÷ 6.10 = 0.96590 = 0.966 4 sig. figs. 3 sig. figs. 3 sig. figs.



Addition and Subtraction with Significant Figures

• When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the lowest number of decimal places


41.5

5214.55799.2

70.0543.2

7.5

976.5

122.0

9.5


Study Buddy Review: S.F. in Calculations

1. Perform the following calculations and express your answer to the correct number of significant digits:

a. 1.27 / 5.296 cm3

b. 12.2 g + 0.38 g

c. 17.3 g + 2.785 g

30.20 cm 3

Study Buddy Review: S.F. in Calculations

1. Perform the following calculations and express your answer to the correct number of significant digits:

a. 1.27 / 5.296 cm3 0.239 g/cm3

b. 12.2 g + 0.38 g 12.6 g

c. 17.3 g + 2.785 g 0.665 g/cm3

30.20 cm 3

Rounding• When rounding to the correct number of significant figures, if

the number after the place of the last significant figure is

a) 0 to 4, round down

– drop all digits after the last sig. fig. and leave the last sig. fig. alone

– add insignificant zeros to keep the value if necessary

b) 5 to 9, round up

– drop all digits after the last sig. fig. and increase the last sig. fig. by one

– add insignificant zeros to keep the value if necessary

• To avoid accumulating extra error from rounding, round only at the end, keeping track of the last sig. fig. for intermediate calculations



RoundingRounding to 2 significant figures

•2.34 rounds to?

2.3

•2.37 rounds to?

2.4

•2.349865 rounds to?

2.3



Scientific Notation:Writing Large and Small Numbers

Move the decimal point to obtain a number between 1 and 10. ( If there is no decimal you may have to add one like below ) Multiply that number (the decimal part) by 10 raised to the power that reflects the movement of the decimal point.

• If the decimal point is moved to the left, the exponent is positive.

• If the decimal is moved to the right, the exponent is negative.

Convert 61300000 to scientific notation

Convert 0.000345 to scientific notation

Convert 5.8 x 105 to standard notation

Convert 2.07 x 10-4 to standard notation

Study Buddy Review

• Convert the following to scientific notation:

0.005 g

10,000 m

• Convert the following to standard notation:

1.5 x 10-3 dL

2.2 x 105mL

Study Buddy Review

• Convert the following to scientific notation:

0.005 g 5 x 10-3 g

10,000 m 1 x 104 m

• Convert the following to standard notation:

1.5 x 10-3 dL 0.0015 dL

2.2 x 105mL 220,000 mL

You are 100% responsible for knowing how to work your calculator

23

EXPEE X 10n

The Metric System

Metric and SI units

• Metric System used in science

• SI System – International System of units based on metric system– Used to standardize quantities between

scientists

Common Units in Chemistry

Quantity it represents

SI unit Common metric unit in Chemistry

Length meter (m) centimeter (cm)

Mass kilogram (kg) gram (g)

Volume m3 (cubic meters)

milliliter (mL)

Temperature Kelvin (K) Celsius (oC)

Common Decimal Prefixes Used with SI Units

Prefix Prefix Symbol

Word Conventional Notation

Exponential Notation

tera T trillion 1,000,000,000,000 1x1012 giga G billion 1,000,000,000 1x109

mega M million 1,000,000 1x106 kilo k thousand 1,000 1x103

hecto h hundred 100 1x102 deka da ten 10 1x101 ----- ---- one 1 1x100 deci d tenth 0.1 1x10-1 centi c hundredth 0.01 1x10-2 milli m thousandth 0.001 1x10-3

micro millionth 0.000001 1x10-6 nano n billionth 0.000000001 1x10-9 pico p trillionth 0.000000000001 1x10-12

femto f quadrillionth 0.000000000000001 1x10-15

Measurements and Calculations Chapter 2. Objectives Construct and use tables and graphs to interpret...

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