metric system measurements significant figures relationships factor label method

Metric systemMeasurements Significant figuresRelationships Factor Label Method

SYSTEM OF MEASUREMENTS (SI)

SI Base Units

Derived SI Units

• Combinations of SI base units form derived units.• pressure is measured in kg/m•s2, or pascals

Temperature can be measured using three different units

Conversion between T units

°F = 9/5 °C + 32

OR

°F = 1.8 °C + 32

K = °C + 273.15

T _ _ G _ _ M _ _ K H D _ d c m _ _ μ _ _ n _ _ p _ _ f

1 kg = 1000 g

e i e i e e e e i i a i er g g l c k c n l c n c ma a a o t a i t l r o o t o i i o o

1 cL = 10000 μL or 1x104 μL

1 dm = 1x108 nm1 kJ = 1x105 cJ

Accuracy and Precision

Three students perform the same experiment:

The density of the metal is 4.2845 g/mL

Density values (g/mL)

Joy Taylor Simon

Trial 1 2.4563 2.2846 4.2867

Trial 2 1.6798 2.2798 4.2904

Trial 3 4.7893 2.2901 4.2896

Accuracy and Precision, continuedPercentage Error• Percentage error is calculated by subtracting the

accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.

Percentage error = Value

experimental-Value

accepted

Valueaccepted

100

• Sample Problem • A student measures the mass and volume of a

substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?

Use of Numbers

• Exact numbers– 1 dozen = 12 things for example

• Accuracy – how closely measured values agree with

the correct value• Precision

– how closely individual measurements agree with each other

Use of Numbers• Significant figures

– digits believed to be correct by the person making the measurement

• Exact numbers have an infinite number of significant figures12.000000000000000 = 1 dozenbecause it is an exact number!!!!

Use of NumbersSignificant Figures - Rules

• Leading zeroes are never significant0.000357 has three significant figures

• Trailing zeroes only significant if after decimal point.2.7800 has five significant figures

• Use scientific notation to remove doubt2.40 x 103 has 3 significant figures

2.400x103 has 4 significant figures

2400 has only two significant figures.

Use of Numbers• Imbedded zeroes are always

significant3.0604 has five significant figures

Use of Numbers

• Multiplication & Division rule Easier of the two rules

Product has the smallest number of significant figures of multipliers

5.22 tooff round

21766.5

31.2x

224.4

3.9 tooff round

89648.3

41.x

2783.2

Sample Problem. Calculate the density of a substance with a mass of 14.78 g and a volume of 10.3 mL

Use of Numbers• Addition & Subtraction rule

More subtle than the multiplication rule

Answer contains smallest decimal place of the addends.

6.95 tooff round

9463.6

20.2

423.1

3692.3

6.671 tooff round

6707.6

312.2

7793.8

Sample problem Determine the perimeter of a piece of paper of 27.94 cm long and 6.92 cm wide.

• Sample Problem • How many significant figures are in each of

the following measurements?

• a. 28.6 g• b. 34.40 cm• c. 910 m• d. 0.046 04 L• e. 0.006 700 0 kg

Chapter 2

•Two quantities are directly proportional to each other if dividing one by the other gives a constant value.

Direct Proportion

Chapter 2Direct Proportion

Two quantities are inversely proportional to each other if multiplying one by the other gives a constant value.

Inverse Proportion

Chapter 2Inverse Proportion

The Unit Factor Method

• Simple but important method to get correct answers in word problems.

• Method to change from one set of units to another.

The Unit Factor Method• fractions represent unit factors

1 ft = 12 in becomes or

in 12

ft 1ft 1

in 12

The Unit Factor Method• Example: Express 9.32 meters in micrometers.

The Unit Factor Method• Example: Express 627 milliliters in L.

The Unit Factor Method• Example: Express 45.8 kg in mg.

Density conversions• Example: A 20.0 g irregular solid is introduced

in a graduated cylinder. The level of water inside the graduated cylinder when from 20.0 mL to 23.3 mL. Calculate the density of the solid.

Density conversions• Example: What volume will occupy a liquid

with a mass of 15.7 g and a density of 1.34g/mL?

Density conversions• Example: Calculate the mass of a gas that

occupies 1.5 L and it has a density of 0.00143g/mL?