Metric system Measurements Significant figures Relationships 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 e i e i e e e e i i a i e r g g l c k c n l c n c m a a a o t a i t l r o o t o i i o o 1 kg = 1000 g 1 dm = 1x108 nm 1 kJ = 1x105 cJ 1 cL = 10000 μL or 1x104 μL

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, continued Percentage 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.

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 Accuracy Precision 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 figures 12.000000000000000 = 1 dozen because it is an exact number!!!!

Significant Figures - Rules Use of Numbers Significant Figures - Rules Leading zeroes are never significant 0.000357 has three significant figures Trailing zeroes only significant if after decimal point. 2.7800 has five significant figures Use scientific notation to remove doubt 2.40 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 significant 3.0604 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

Sample Problem. Calculate the density of a substance with a mass of 14 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.

Sample problem Determine the perimeter of a piece of paper of 27 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 Direct Proportion Two quantities are directly proportional to each other if dividing one by the other gives a constant value.

Chapter 2 Direct Proportion

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

Chapter 2 Inverse 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

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?