Unit 0 Section 1: Observations & Measurement
Taking Observations
Qualitative Data / Quantitative DataQualitative data
· Clear vs. Colorless
· Colorless does not describe transparency
Clear / Cloudy / OpaqueWords to Describe Transparency
SELF CHECK: Describe the following in terms of transparency words & colors
1. Cherry Kool-Aid: ______
2. Milk: ______
3. Water: ______
Gathering Data
· Quantitative measurements use the metric system; see chart for common measurements
Measurement / Instrument / Most Common UnitMass
Volume
Temperature
Length
Time
Uncertainty in Measurement Making Measurements
® A measuring instrument can have different calibrations.
® The more lines on an instrument, the more ______an instrument and the better a measurement.
a) ______ml
b) ______ml
c) ______ml
® Every measurement has a degree of uncertainty. The last number you write down is an estimated number
® Remember: Always read liquid levels at eye level from the bottom of the ______
® Keep it Simple
o Write down a “5” if the measurement is in-between lines
o Write down a “0” if the measurement is exactly on the line
o The volume of the liquid in the figure to the right is : ______ml
Example: Measure the length of the following rulers.
[1] Ruler A: ______m
[2] Ruler B: ______m
Measuring Volume
Example: Measure the temperature on the thermometer B [right].
______° C
Measuring Mass
ü Always read exactly what you see on the balance. There is no need to estimate the last digit.
Unit 0 Section 2
Accuracy & Precision of Measurement & Significant Figures
Measurements must be:
o Accurate = getting the “correct” answer; how close your measurement is to the “accepted value”
o Precise = getting consistent data within experimental error; being able to reproduce a measurement
Multiple trials help ensure that you’re results weren’t a one-time fluke!
Example: Describe each group’s data as accurate or precise. The accepted value is the bulls-eye.
Is it accurate?Is it precise?
Percent Error: a calculation used to measure accuracy
Percent Error = / x 100 / Remember! “Accepted” also known as “theoretical”Example:
Below is a data table produced by three groups of students who were measuring the mass of a paper clip, which had a known mass (accepted value) of 1.0004g.
Group 1 / Group 2 / Group 3 / Group 41.01 g / 2.863287 g / 10.13251 g / 2.05 g
1.03 g / 2.754158 g / 10.13258 g / 0.23 g
0.99 g / 2.186357 g / 10.13255 g / 0.75 g
Average / 1.01 g / 2.601267 g / 10.13255 g / 1.01 g
Which group represents a properly accurate and precise measurement of the mass of the paper clip?
SELF CHECK!
A student measured an unknown metal to be 1.50 grams. The accepted value is 1.87 grams. What is the percent error?
Significant Digits (Significant Figures)
Definition all the digits in a measurement known with certainty plus one final digit, which is uncertain or is estimated
® A significant digit is any measurement made in lab
® The real purpose of “significant digits” is ______
______
______
Rules to Count Significant Digits
[1] All nonzero numbers are significant & middle zeroes (zeroes contained between non-zero numbers) are significant
Example: 300042 ______
[2] Leading zeroes are never significant.
Example: 0.000034 ______
[3] Trailing zeroes are significant if there is a decimal place anywhere in the problem.
Example: 0.0002500 ______
[4] Trailing zeroes are not significant if there is no decimal place.
Example: 190000 ______0.004004500 ______
Another Example: 0.004004500 ______
Over Simplification Rule: Not mentioned in video-we will go over in class
o If there is no decimal point in the number, count from the first non-zero number to the last non-zero number
o If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end
SELF CHECK!
How many significant digits are in the following?
7007 / 0.00205 / 10.320250 / 250. / 6.8700 x 104
Unit 0 Section 3
Rounding & Calculating with Significant Figures
Rules to Rounding Significant Digits
[1] What place are you rounding to? Circle it!
[2] What is the neighbor #? Underline it!
[3] Look at the neighbor # and remember
5 or more, raise the score
less than 5, let it lie
[4] After rounding the place, all neighbors to the right are dropped to the right of a decimal number; if a whole number, all neighbors to the right become zeroes
Example: Round 4682 to the hundred’s place ______
SELF CHECK!
Round to the number of significant digits in the parentheses.
0.00254 (3) / 5.05 (2)6578 (3) / 120004.25 (3)
Calculations with Significant Digits
o When recording a calculated answer, you can only be as precise as your least precise measurement
ü Addition & Subtraction: Round your answer to the least number of decimal places to the right of the decimal point that appeared in the problem.
Examples:
1.457 + 83.2 = ______
0.0367 - 0.004322 = ______
ü Multiplication & Division: Round the answer to the least number of significant figures that appeared in the problem
Examples:
4.36 x 0.00013 = ______
12.300/0.0230 = ______
SELF CHECK!
Compute & write the answer with the correct number of significant figures
0.045 + 1.2 / 1.000/2.342.5 x 23.5 / 6.732 - 0.23
Multi-Step Calculations
o Always complete the calculations first, and then round at the end!
ü 6.68 x 1.2/ 14.8 = .5416216216 in the calculator à round to 2 sig figs à .54
o EXCEPTION: When adding/subtracting and then multiplying/dividing, follow the rules for addition/subtraction first and then apply that number of sig figs to the multiplication/division.
(14.991- 14.98)/14.991 = ______
Unit 0 Section 4
Density
® Density is defined as the ______of mass to volume of a sample.
How Heavy is it for its size:
LEAD = ______= small size is very heavy
AIR = ______= large sample has very little mass
Density Equation:® Substances ______when they are less dense than the substance they are in. Using density values, Is water more or less dense than vegetable oil? ______
® Look at the density values to compare the various densities of substances. The larger the density, the more dense!
® Density does vary with ______.
Why? Most substances will expand when heated, increasing the volume and decreasing the density.
But ______is an exception. As water cools, it expands, increasing the volume and decreasing the density…….. Ice Floats on water
Calculating Volume using Water Displacement
v You can measure the volume of an object by water displacement. The volume is the difference between the ______and initial volume of the water after the object has been added to the water.
Examples:
Example 1: What is the density of a sample with a mass of 2.50g and a volume of 1.7 ml?
Example 2: What is the mass of a 2.34 ml sample with a density of 2.78 g/ml?
Example 3: A sample is 45.4 g and has a density of .87 g/ml. What is the volume?
Self-Check:
Is it Aluminum? The metal has a mass of 612 g and a volume of 345 cm3? Aluminum’s density =2.70g/cm3
Graphing Density
Slope of a line = ______so
Slope = Density / Mass (DY)Volume (DX)
1. Pick 2 points on the best fit line
2. Calculate DY ( 11.25 -3 = 8.25g)
3. Calculate DX ( 11-3 = 8 ml)
4. Plug into above equation and divide to solve for density . (8.25g/8 ml = 1.03 g/ml)
Unit 0 Section 5
The Metric System & Conversions
o Universal system of measurements
o Based on the power of 10
Metric Prefixes
o Used to describe smaller or larger amounts of the base units
Other PrefixesTHE / GREAT / MAGISTRATE
Tera / Giga / Mega
T / G / M
1x 1012 / 1 x 109 / 1 x 106
Basic Prefixes
KING / HENRY / DIED / BY / DRINKING / CHOCOLATE / MILK
Kilo / Hecto / Deka / Base
Unit / deci / centi / milli
K / H / Da / 1 / d / c / m
1000
Other Prefixes
MONDAY / NEAR / PARIS
Micro / Nano / Pico
u / n / p
1x 10-6 / 1 x 10-9 / 1 x 10-12
Base Units
ü have a value of 1
ü Examples are the liter ______, meter______, gram ______,second ______
ü Place a prefix in front of the base unit for a larger or smaller number.
Example: ks = kilosecond mm = millimeter cg = centigram
Using Ladder Method: Converting with the Metric System By Moving a Decimal Point
1. Determine the starting point.
2. Count the jumps to your endpoint.
3. Move the decimal the same number of jumps in the same direction
4. If using the “other” prefixes, remember that there is a difference of 1000 or 3 places between each.
Example:
[1] 4km = ______m
You Try:
[1] Convert 15 cl into ml ______
[2] Convert 6000 mm into Km ______
[3] Convert 1.6 Dag into dg ______
A different way of converting between units
· Dimensional Analysis is another method for converting between different unit
· Dimensional Analysis uses equivalents called ______to make the exchange.
Change the Equivalents to Conversion Factors
1 feet = 12 in ______4 quarters = 1 dollar ______
Steps for using Dimensional Analysis
1. Begin with what you have: Write down your given information
2. Determine what you want.
3. Use or create a conversion factor to compare what you have to what you want.
4. Set up the math so that the given unit is on the bottom of the conversion factor & the desired unit is on top. Plug in the values of the conversion factor.
5. Calculate the answer…multiply across the top. Multiply across the bottom. Divide the top by the bottom.
Canceling Units in DA
® Any unit that is identical on the top and the bottom of an expression will cancel
® When canceling units…just cancel the units…
Example: How many grams are equal to 127.0 mg?
Multi Step Problems
® Occur when there isn’t always an equivalent that goes directly from where you are to where you want to go
® With multi-step problems, it’s often best to plug in units first, then go back and do numbers.
Example
[1] How many kilograms are equal to 345 cg?
SELF CHECK!
[2] How many grams are equal to 0.250 Kg
Unit 0 Section 6
Scientific Notation
® Scientific Notation is a form of writing very large or very small numbers
® Scientific notation uses powers of 10 to shorten the writing of a number.
Changing Numbers to Scientific Notation
® The decimal point is moved to make a number between 1 and 10
® The power of 10 is the number of times it moved to get there
® A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent
Example
Write the following numbers in scientific notation.
240,000 ______0.0000048 ______
Reading Scientific Notation- changing it to Standard Form
® A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller
® Move the decimal place to make the number bigger or smaller the number of times of the power of ten
5.3 x107 ______
SELF CHECK!
Write out the following numbers in scientific notation on the left & ordinary notation on the right.
[3] 123000000 ______
[4] 0.000987 ______
[5] 0.00000612 ______
[6] 0.000000045 ______
[7] 480000000000 ______
[8] 3.4 ´ 10-9 ______
[9] 1.12 ´ 105 ______
[10] 2.347 x107 ______
[11] 8.9 x 10-3 ______
[12] 7.23 ´10-12 ______
We will do this section in class!
® Sometimes there isn’t a way to write a number with the needed number of significant digits UNLESS YOU USE SCIENTIFIC NOTATION
® Write 120004.25 m with 3 significant digits ______
How to do calculations in scientific notation in your scientific calculator:
[1] Punch the number (the digit number) into your calculator.
[2] Push the EE or EXP button. Do NOT use the x (times) button!
[3] Enter the exponent number. Use the +/- button to change its sign.
Practice: Multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer is ______