Measurement/Calculation

Units of Measure

Metric System

• based on powers of ten, so it’s easy to convert between units.

• Remember:– KING HENRY DANCED BEFORE DAWN

COUNTING MONEY – Or– KING HENRY DIED BY DRINKING

CHOCOLATE MILK

Units

Mega kilo hecto deka BASE deci centi milli micro

M k h da (none) d c m

106 105 104 103 102 101 100 or 1

10-1 10-2 10-3 10-4 10-5 10-6

How to use

KiloHecto

DekaBASE

Deci

Centi

MilliLeft

Right

Examples

• 20 L= _______ mL

• 7 kg = _______ mg

• 90 mm = _______ cm

• 223 mL = ________ L

• 0.49 hm = ______ m

MilliCenti

DeciBASE

DekaHecto

Kilo

20 000

7 000 000

9.0

0.223

49

SI base units

Quantity Base Unit Symbol

Time second s

Length meter m

Mass kilogram kg

Temperature Kelvin K

Amount of a substance mole mol

SI derived units

Quantity Derived Unit Symbol

Volume: various formulas, such as LxWxH

cubic centimeters or millilitersliters

cm3 or mLL

Density: mass divided by volume

grams per milliliter or grams per cubic centimeter

g/mL or g/cm3

(derived units are calculated from base units)

NOTE:

• 1 cm3 IS EQUAL TO 1 mL!!!

• And a cc is the same as a cm3

Measurement/Calculation

Scientific Notation/Accuracy &Precision

Rules to putting into Sci Not

• Must have a whole number between 1- 9

• If you move:

– Decimal to Left…exponent is Positive

– Decimal to Right...exponent is Negative

Examples

• .0032

• 15 300 000 1.53 X 107

3.2 X 10-3

Examples

• 5.00 X 104

• 2.32 X10-3

5.00 0050 000

2.320 0.00232

Addition/Subtraction

• Make exponents the same by moving decimal place and changing exponent

• Then add/subtract and put in correct Sci Not

OR

Type into your calculator

Change mode to Sci

Example

5.00 X 104

+ .244 X 104

ORType into your calculator

5.00 X 104

+ 2.44 X 103

5.244X 104

5.00EXPEXP

EEEE 4 ++ 2.44EXPEXP

EEEE 3 EnterEnter

Multiplication/Division

• Multiplication– Multiply numbers– Add exponents

• Division– Divide numbers– Subtract exponents

• Then put back in correct scientific notation!

Example(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:

=0.67 X 103 g/mol = 6.7 × 102 g/mol

Accuracy and Precision

• Accuracy: how close a measurement is to the true value (the “correct answer”)

• Precision: how close a value is to other values in that series

Are the following groups of measurements accurate, precise, both, or neither?

1) Given: true mass of sample of zinc is 14.5 gMeasurements made:

13.2 g, 15.6 g, 17.9 g, 12.0 g2)Given: true volume of sample of water is

33.3mLMeasurements made:

22.4 mL, 22.2 mL, 22.4 mL, 22.3 mL3) Given: true length of copper wire is 58.5 cm

Measurements made: 58.4 cm, 58.5 cm, 58.5 cm, 58.4 cm

Qualitative: a descriptive measurement (quality); does not involve numbers

Quantitative: a numerical measurement (quantity)

Measurement/Calculation

Significant Figures

Rules to Significant Figures

• If it’s not 0, it counts.

• Example• 743.44• 24

5

2

Rules to Significant Figures

• 0’s in between significant figures count.

• Example• 506• 20405

• .707

3

5

3

Rules to Significant Figures

• All 0’s at the end past the decimal point count.

• Example• 2.440• 784.30

4

5

Rules to Significant Figures

• 0’s as placeholders don’t count.

• Example• 440• 0.09 1

2

Alternative Way

Pacific

(Present)

Atlantic

(Absent)

• If the decimal is present, start on the Pacific side at the first nonzero digit and count it and all the digits to the right of it.

• If the decimal is absent, start on the Atlantic side at the first nonzero digit and count it and all the digits to the left of it.

Pacific

(Present)

Atlantic

(Absent)

Adding/Subtracting

• Add/Subtract First• The answer has only as many decimal

places as the measurement having the least number of decimal places.

• Example 190.2 g

65.291 g 12.38 g 267.871 g

13

2

Answer should have 1 decimal place

267.9 g

Multiplication/Division

• The answer has only as many significant figures as the measurement with the least number of significant figures.

• Example13.78 g

11.3 mL

4

3

= 1.219469 g/mL Answer should have 3 significant figures

1.22 g\ml

Mult/Divide First

• Example– 15000

– 2030.0

– 0.0020

2

5

2

Measurement/Calculation

Density

Density

• Derived unit – g/mL or g/cm3

• Mass/Volume

m

DV

D. Density

• An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

m = ?

WORK:

m = DV

m = (13.6 g/cm3)(825cm3)

m = 11 220 g=11 200g

mD

V

D. Density

• A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

m = 25 g

WORK:

V = m D

V = 25 g

0.87 g/mL

V = 28.74mL = 29 mL

mD

V

D. Density1. A marble has a mass of 5.6 g. It is placed

in a graduated cylinder with 50.0 mL of water. The water level rises to 53.4 mL. What is the density of the marble?

GIVEN:

D = ?

V = 53.4-50 =3.4 mL

m = 5.6 g

WORK:

D = m V

D = 5.6 g

3.4 mL

D=1.647 g/mL = 1.6 g/mL

mD

V

3.4 mL

GraphingGraphing is an important tool for expressing data so that it is easier to read and interpretRules for graphing:--place the manipulated/independent variable (the one that was changed) on the x axis.--place the dependent/responding variable (the results of that change) on the y axis.(dry mix)

DRY

MIX

y scale = largest y value – smallest y value x scale = largest x value – smallest x value# of lines on the y axis # of lines on the x axis

The graph should cover at least ¾ of the grid