Measurement and Calculation

Unit 2

The Fundamental SI UnitsThe Fundamental SI Units (la Système Internationale, SI)(la Système Internationale, SI)

Physical Quantity Name Abbreviation

MassLength

Time

Temperature

Electric Current

Amount of Substance

Luminous Intensity

kilogram

meter

second

Kelvin

Ampere

mole

candela

kg

ms

K

A

mol

cd

SI UnitsSI Units

SI PrefixesCommon to Chemistry

Base unit1

100

Deci (d)1/1010-1

Centi (c)1/10010-2

Milli (m)1/1000

10-3

Micro (μ)1/1000000

10-6

Nano (n)10-9

Pico (p)10-12

Kilo (k)1,000103

Mega (M)1,000,000

106

Giga (G)1,000,000,000

109

Scientific Notation• A shorthand method of expressing large and

small numbers using exponents.• Expresses values as a multiple of 10 to a

specific power. Must use the correct form when expressing a number in sci not.

M x 10n

M = any number between 1 & 10n = any integer (including 0)

• Example: 12,480,000 → 1.248 x 107

0.0000237 → 2.37 x 10-5

Scientific Notation

• Express the following in scientific notation:1. 2,300,0002. 0.00401Express the following in decimal form:1. 6.01 x 103

2. 6.01 x 10-4

Scientific Notation• Perform the following

calculations, expressing your answer in scientific notation.

1. (6.0 x 104) (2.0 x 105)

2. (1.248 x 107)(2.37 x 10-4)

3. (8.0 x 103) / (2.0 x 106)

4. (2.0 x 10-3) / (4.0 x 10-8)

5. (5.27 x 104) + (2.96 x 106)

1.2 x 1010

2.96 x 103

4.0 x 10-3

5.0 x 104

3.01 x 106

Accuracy vs. Precision

• Accuracy refers to how close a measurement is to the true or actual value.

• Precision refers to how close a series of measurements are to one another.

Reporting Measurements

• To indicate the uncertainty of a single measurement scientists use a system called significant figures

• Our data can only be as precise as the least precise measuring tool/instrument

Rules for Counting Significant Figures

1. Nonzero integers are always significant

Ex. 46.3 m 3 sig figs

6.295 g 4 sig. figs

2. ‘0’ between nonzero digits are significant.

Ex. 40.7 L 3 sig. figs.

87009 km 5 sig figs

Rules Continued

3. ‘0’ in front of nonzero digits (leading zeros) are never significant.

Ex. 0.009587 m 4 sig. figs. 0.0009 kg 1 sig. fig.

Neither are zeroes at the end of a numberEx. 1300 g = 2 sig figs

*The zeroes in these cases are ‘placeholders’; they are used for spacing.

Rules Continued

4. Zeros at the end of a number and to the right of a decimal are significant.

Ex. 85.00 4 sig. figs. 9.070000000 10 sig. figs.

5. A decimal point placed after zeros indicates that the zeros are significant.

Ex. 2000 1 sig. fig 2000. 4 sig. figs.

Rules Continued

• Do NOT count sig. figs. in the following numbers:

1. Counting numbers

2. Constants which are defined values (1 atm)

3. Conversion factors which are defined relationships (1km = 1000m)

Calculations with Significant Figures

• Answers to calculations must be rounded to the proper number of significant figures at the end of the calculation.

Adding/Subtracting Numbers with Significant Figures

• When adding/subtracting, look for the LEAST PRECISE measurement to determine the correct number of sig. figs.

• Round answer to the same decimal place

Ex. 54 g + 108.6 g + .0004 g = 163 g

55.24 mL – 2.1 mL = 53.1 mL

Multiplication/Division with Significant Figures

• Count the number of significant figures in each measurement

• Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures

4.5 x 0.200 = 2 sf 3 sf

0.90

4.13 x 104 ÷ 0.07000 = 590000= 5.90 x 105

Correct?

How HOT are you??

• Heat (energy) cannot be measured directly.

• We can measure heat transfer by change in temperature.

• We define temperature as the average kinetic energy of a system.movement within a substance

• Measure temperature with a thermometer.

Temperature Scales• Fahrenheit Scale, °F

Relative scale

• Celsius Scale, °CRelative scaleWater’s freezing point = 0°C, boiling point = 100°C

• Kelvin Scale, KAbsolute scaleWater’s freezing point = 273 K, boiling point = 373 K

• oC = K - 273 K = oC + 273

Graphing

1. Determine the variables.- Independent x-axis- Dependent y-axis

2. Determine the range of values.

3. Utilize all of 1 side of the graph paper.- usually start at ‘0’ but NOT ALWAYS

4. Makes scales easy & keep consistent

Graphing

5. Label both axes (include unit).

- draw axes with a straight edge

6. Give your graph an appropriate title.

- dependent vs. independent

7. Titles, axes, & labels must be in INK!

8. Plot data with ‘x’ not ‘•’ (may be in pencil)

9. Draw “best-fit” line (or curve) through your data

Graphing

10. You may be asked to use your graph to

draw conclusions & make predictions.

• Three examples would include:Interpolation – within the limits of the dataExtrapolation – beyond the limits of the dataSlope Determination (show work on graph)

“Best-Fit” Line

                                                

                                                

                                                

                                                

                                                

                                                

Distance vs. Time for Freefall

Temperature of Water Graph• Construct a graph of the data that was collected.

oF on the y-axis oC on the x-axis

• Draw best-fit line through data points.• Calculate the slope of the line and show your

calculations on the graph.• Use the slope and the y-intercept to write the

equation of the line (y = mx + b). What does this equation represent?

• What is the 0C that is equivalent to 0oF (determine this by using the graph itself)? What graphing technique did you use to determine this?

Dimensional Analysis

• A simple mathematical approach to converting between units.

• Involves conversion factors (fractions).• Follows simple math functions (x/÷)• We can use conversion factors for metric conversions

as well as other conversions.• Dim. analysis can be used to convert from 1 unit to

another.One step or several steps.

• Each conversion factor represents a math function – treat it as such.

Dimensional Analysis

• Examples:

1. What is the volume of a 250-mL beaker in L?

2. What is your weight in g?

3. How many kg are equivalent to 4 lbs?

4. How many mg are in .500 lbs?

5. How many lbs are equivalent to 4.00 kg?

Density• Density is a property of matter representing the mass

per unit volume• For equal volumes, denser object has larger mass• For equal masses, denser object has small volume• Solids = g/cm3

1 cm3 = 1 mL• Liquids = g/mL• Gases = g/L

1L = 1 dm3

• Volume of a solid can be determined by water displacement

Volume

MassDensity

Using Density in Calculations

Volume

MassDensity

Volume Density Mass Volume

Mass Density

Density = Mass Volume

Volume = Mass Density

Brownie Graph

1. Graph mass (y) vs. volume (x)

2. Draw best-fit straight line through data points. Extend to y-axis

3. Calculate slope (decimal # and units) – show work on graph

4. Answer the following:

- What does the value for the slope represent?

- What is the value for the y – intercept?

- What does it represent?