CHAPTER 2

ANALYZING DATA

SI MEASUREMENT

SI (def): Le Systeme International d’ Unites (International System of Units)

SI has 7 base units and almost all other units are derived from these.

SI MEASUREMENT

QUANTITY QUANTITY SYMBOL

UNIT NAME

UNIT ABBREVIATION

Length l meter m (not italicized)

Mass m(italicized)

kilogram kg

Time t second s

Temperature T Kelvin K

SI MEASUREMENT

QUANTITY QUANTITY SYMBOL

UNIT NAME

UNIT ABBREVIATION

Amount of substance

n mole mol

Electric current

I ampere A

Luminous intensity

IV candela cd

SI MEASUREMENT

Prefixes are added to the base units to represent larger or smaller quantities.

Table 2.2: SI Prefixes, pg. 33

MUST MEMORIZE

SI MEASUREMENT

SI MEASUREMENT

SI units are defined in terms of standards of measurement. They are either objects or consistent natural phenomena.

International organizations monitor the defining process. In the US, the National Institute of Standards and Technology plays a major role in setting standards

DERIVED UNITS

1) Derived SI units: combinations of SI base units

Examples:

density = mass

volume

DERIVED UNITS

2) volume: amount of space occupied by an object

non-SI volume unit:

liter, L 1 L = 1000 cm3

SI volume unit: m3

DERIVED UNITS 3) density: mass per unit volume

d = m/V

Mass and volume change proportionately, meaning that the ratio of m to V is constant. Density is an intensive property.

Density and temperature: at high T, most objects expand.

SCIENTIFIC NOTATION

Scientific Notation: numbers written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number.

65 000 km 6.5 x 104 km

0.0012 mm 1.2 x 10-3 mm

Scientific Notation Rules

To find M: Move the decimal point in the original # to the left or right so that only one nonzero digit remains to the left of the decimal point

To find n: Count the # of places that you moved the decimal point

(Moved left, n = + Moved right, n = - )

SCIENTIFIC NOTATION

Addition and Subtraction: Values must have same value exponent before you can do these operations

Multiplication: M factors are multiplied and exponents are added

Division: M factors divided and exponent of denominator subtracted from exponent of numerator

3

3

cm

gcm

Dimensional Analysis

The “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g

Dimensional Analysis

Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

Dimensional Analysis

Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

Dimensional Analysis

How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

Dimensional Analysis

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

Dimensional Analysis

How many liters of water would fill a container that measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L

1000 cm3

Dimensional Analysis

5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in

2.54 cm= 3.2 in

cm in

Dimensional Analysis

6) Taft football needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

Dimensional Analysis

7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1.3 m 100 cm

1 m= 86 pieces

cm pieces

1 piece

1.5 cm

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

ERROR

B. Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

% Error Problems

Try the two practice problems on the outline.

Percent Error Examples

a. What is the % error for a mass measurement of 17.7 g if the correct value is 21.2 g?

17.7 g – 21.2 g x 100 =

21.2 g

b. A volume is measured experimentally to be 4.26 mL. What is the % error if the correct value is 4.15 mL?

4.26 mL – 4.15 mL x 100 =

4.15 mL

ERROR IN MEASUREMENT

In any measurement, some error or uncertainty exists

Measuring instruments themselves place limitations in precision

Estimate the final questionable digit.

D. 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

Significant ≠ Certain

Must memorize the rules for recognizing significant figures!

SIG. FIGS. RULESRULE EXAMPLE

1. No zeros, All sig. 852 m 97.25 mL

2. Zeros between nonzero digits = sig.

40.7 L 87009 km

3. Zeros at front of nonzero digits ≠ sig.

0.095897 m0.0009 kg

4. Zeros at end of # and to right of decimal = sig.

85.00 g9.000 000 000 mm

5. Decimal after zeros, sig. Zeros with no decimal ≠ sig

2000 m2000. m

Atlantic-Pacific Check

Pacific, Atlantic,

Decimal is Decimal is

Present Absent

Significant figures practice

Try the practice problems on the outline

Sig. Figs. Practice

a) 804.05 g

b) 0.0144030 km

c) 1002 m

d) 400 mL

e) 30000. cm

f) 0.000625000 kg

ROUNDING RULES

Digit after last digit to be kept:

Last digit should: Examples (3 sig. Figs)

> 5 Increase by 1 42.68 g 42.7 g

< 5 Stay the same 17.32 m 17.3 m

5, followed by nonzero

Increase by 1 2.7851 cm 2.79 cm

5, preceded by odd

Increase by 1 4.635 kg 4.64 kg

5, preceded by even

Stay the same 78.65 mL 78.6 mL

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 7.8 mL

3.75 mL

+ 4.1 mL

7.85 mL

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

Sig. Figs./Rounding Practice

Try the practice problems on the outline.

Practice Problems

1. What is the sum of 2.099 and 0.05681?

2. Calculate the quantity 87.3 cm – 1.655 cm

3. Polycarbonate has a density of 1.2 g/cm3. A photo frame is constructed from two 3.0 mm sheets. Each side measures 28 cm by 22 cm. What is the mass of the frame?

Conversion Factors

Conversion factors are typically exact.

Do not count when determining # of significant figures in answer.

E. Proportions

Direct Proportion

Inverse Proportion

xy

xy

1

y

x

y

x

Direct and Indirect Proportions

Direct: 2 quantities are directly proportional if dividing one by the other gives a constant value; graph is a straight line, y/x = k

Indirect: 2 quantities are indirectly proportional if their product is constant, graph curved, xy = k or y α 1/x

GRAPHS