Chapter 2

Data Analysis

Section 2.1

Units of Measure

SI Units

• Le Système Internationale d’Unités (SI)• Based mostly on the French metric system• SI Units can be base units or derived units

Base Units

• A defined unit that is based on an object or event in the physical world.

• Independent of other units-Time – the SI base unit is the second (s)-Length – the SI base unit is the meter (m)-Mass – the SI base unit is the kilogram (kg)

Derived Units

• A unit that is defined by a combination of base units

• Dependent on other units- Volume – can be measure in cm3, dm3, or

Liters (L)- Density – measured in g/mL, or g/cm3

SI Unit Prefixes

Prefixes are sometimes added to make lengths more appropriate for measuring

Practice

1) How many millimeters are in one meter?2) How many meters are in one megameter?3) How many millimeters are in one

megameter?4) How many meters are in one centimeter?5) How many kilometers are in one meter?6) How many kilometers are in one centimeter?

Density

• Density is the ratio of mass to volume of an object.

• The density of a specific substance does not change

• A less dense substance will float on a more dense substance.

Density

• Density is calculated using the equation

• Density (ρ) = mass/volume

Practice Density1) You have a rock with a volume of 15cm3 and a mass of 45 g. What is its

density?2) A rectangular block of copper metal weighs 1896 g. The dimensions of the

block are 8.4 cm by 5.5 cm by 4.6 cm. From this data, what is the density of copper?

3) 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, From this information, calculate the density of iron.

4) If 30.943 g of a liquid occupy a space of 35.0 ml, what is the density of the liquid in g/cm3?

5) How many cm3 would a 55.932 g sample of copper occupy if it has a density of 8.92 g/cm3?

6) What is the mass of the alcohol that exactly fills a 200.0 mL container? The density of alcohol is 0.789 g/mL.

7) Find the mass of 250.0 mL of benzene. The density of benzene is 0.8765 g/mL.

Section 2.2

Scientific Notation and Dimensional Analysis

Scientific Notation

• Expresses numbers as a multiple of two factors: a number between 1 and 10 (the coefficient); and ten raised to a power

• 602,000,000,000,000,000,000,000• Easier to write as 6.02x1023 • Used to make very “bulky” numbers easier to

write• 0.000 000 000 000 000 000 000 000 001 672 62kg

is easier written as 1.67262x10-27

Practice

• Convert these numbers into scientific notation1) 700m 2) 4,500,000m 3) 0.0054 kg4) 0.000 006 87 kg

• Convert these numbers into decimal form1) 1.56x103 2) 6.7x1014 3) 4.565X10-2 4) 9.64X10-11

Dimensional Analysis

• Used to convert from one unit to an equivalent value of another unit

• For example: If I have 2.5 dozen eggs, how many eggs do I have?

• We need a conversion factor to convert from dozens of eggs to single eggs.

1 dozen = 12 units or 12 units = 1 dozen.Conversion factors set up equivalent values of different units.

They can also be written like so: or units

dozen

12

1

dozen

units

1

12

• When you convert from one unit to another1) Determine what you are given to start with2) Determine a conversion factor from our starting units

to another unit3) Determine how the conversion factor should be set

up (what goes on top, what goes on bottom)4) Carry out the operation5) If the units we have after the conversion are not our

ending units, repeat steps 2-5 until we arrive at our intended units

Practice

• On page 34 and 35, do numbers, 17-21 for some light practice.

Section 2.3

How reliable are measurements?

Accuracy and Precision

• Accuracy is how close a measurement is to its standard value

• Precision is how close a series of measurements are to each other

• One can be accurate, but not precise; precise but not accurate; both; or neither

• Think of a dartboard

Percent Error

• Scientists must often determine the precision and accuracy of their experiments.

• Imprecise or inaccurate data can mean the difference between a success and a failure

• Scientists use a calculation called percent error to evaluate the accuracy of their data

• Percent error is the ratio of an error (the difference between their actual results and their expected results) and the expected value

Percent Error

• Percent error is calculated through the following equation:

%100% xvalueaccepted

errorerror

Practice

• On page 38, do problems 29 and 30

Significant Figures

• Significant figures are a way for scientists to indicate the precision of their measurements

• 3.52 is a more precise measurement than 3.5• Sig figs include all known digits plus one

estimated one

If we look at this graduated cylinder measurement, we know for a fact that this is measurement is between 30.3mL and 30.4mL, so to indicate this we estimate where between 30.3mL and 30.4mL to show the precision of our answer. We might estimate that this value is 30.32mL. The last two is our ESTIMATED digit, indicating that we are certain of everything before that

The Atlantic-Pacific Rule for Sig Figs

The easy way to remember sig fig rules is to remember the Atlantic-Pacific rule

Atlantic rule – if the decimal is absent, go to the Atlantic side of the number (the right side) and move left until the first non-zero digit. That digit and all digits to its left are significant7600 has 2 s.f.75621 has 5 s.f.

Pacific rule – if the decimal is present, go to the Pacific side of the number (the left side) and move right until you reach the first non-zero digit. That digit and all digits to its right are significant0.0012 has 2 s.f.1.2 has 2 s.f.

Adding and Subtracting with Sig Figs

• When adding or subtracting with sig figs, the solution should carry the same number of decimal points to the right of the decimal as the value with the fewest number of decimal places

Multiplying and Dividing with Sig Figs

• When multiplying and dividing with sig figs, the solution should have the same number of sig figs as the value with the least number of sig figs.

Sig Figs and Scientific Notation

• All digits of the coefficient of a number written in scientific notation are always significant.

6.02x1023 has 3 sig figs1.0x101 has 2 sig figs

Practice

• Determine the number of sig figs in each of the following numbers

0.005641200012000.1.283014532.1200

Practice

• Determine the answer with the correct number of sig figs

1.03+1.42.18-2.1145-38.61563/412.565.3*0.01563

Interpreting Graphs

Interpreting Graphs

Interpreting Graphs