1. The Numbers of Science
Data Analysis

2. Measurements and Units

3. Units of Measure SI units: Systeme Internationale d’ Unites
standard units of measurement to be understood by all scientists
Base Units: defined unit of measurement that is based on an object or event in the physical world
there are 7 base units
some familiar quantities are time, length, mass, and temp

4. Time
second (s)
Many chemical reactions take place in less than a second so scientist often add prefixes, based on multiples of ten, to the base units.
ex. Millisecond
Length
meter (m)
A meter is the distance that light travels though a vacuum in 1/ of a second.
What is a vacuum?
Close in length to a yard.
Prefixes also apply…ex. millimeter

5. Mass mass is a measurement of matter kilogram (kg) about 2.2 pounds
Masses measured in most laboratories are much smaller than a kilogram, so scientists use grams (g) or milligrams (mg).
How many grams are in a kilogram?
1000
How many milligrams are in a gram?

6. Derived Units Not all quantities are measured in base units
A unit that is defined by a combination of base units is called a derived unit.
Volume and Density are measured in derived units.

7. Volume The space occupied by an object Unit = cm3 = mL
Liters are used to measure the amount of liquid in a container (about the same volume as a quart)
Prefixes also applied…ex. milliliter

8. Density Density= mass/volume
The ratio that compares the mass of an object to its volume is called density.
Units are g/cm3
You can calculate density by the following equation:
Density= mass/volume
Ex: What is the density of a sample of aluminum that has a mass of 13.5 g and a volume of 5.0 cm3?
Density= 13.5g/5.0cm3
=2.7g/cm3

9. We also use the Celsius (C) scale
Temperature
A measurement of how hot or cold an object is relative to other objects
The kelvin (K) scale
water freezes at 273K
water boils at 373K
We also use the Celsius (C) scale
water freezes at 0oC
water boils at 100oC

10. To Convert Celsius to Kelvin…
Add 273!!
ex: -39oC + 273= 234 K
To Convert Kelvin to Celsius…
Subtract 273!!
ex: 234K- 273= -39°C

11. Dimensional Analysis

12. Dimensional Analysis Conversion factor:
A numerical factor used to multiply or divide a quantity when converting from one system of units to another.
Conversion factors are always equal to 1
Dimensional analysis:
A fancy way of saying “converting units” by using conversion factors

13. Dimensional analysis often uses conversion factors
Suppose you want to know how many meters are in 48 km. You have to choose a conversion factor that relates kilometers to meters. You know that for every 1 kilometer there is 1000 meters. What will your conversion factor be? 1000m/1km Now that you know your conversion factor, you can multiply it by your known…BUT you want to make sure you set it up so that kilometers cancels out. How would you do this?

14. 48km x 1000m 1km =48,000 m TIP: Put the units you already have on the bottom of the conversion factor and the units you want on top.

15. Scientific Notation

16. Scientific Notation
Numbers that are extremely large can be difficult to deal with…sooo
Scientists convert these numbers into scientific notation
Scientific notation expresses numbers as a multiple of two factors:
A number between 1 and 10 (only 1 digit to the left of the decimal!)
Ten raised to a power

17. For example:
A proton’s mass = kg
If you put it in scientific notation, the mass of a proton is expressed as x kg
Remember:
When numbers larger than 1 are expressed in scientific notation, the power of ten is positive
When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative

18. Try these: Convert 1,392,000 to scientific notation. = 1
Try these: Convert 1,392,000 to scientific notation. = x 106 Convert 0.000,000,028 to scientific notation. = 2.8 x 10-8

19. Adding and Subtracting using Scientific Notation
Make sure the exponents are the same!!
7.35 x x 102 = 9.78 x 102
If the exponents are not the same, you have to make them the same!!
Tip: if you increase the exponent, you decrease the decimal if you decrease the exponent, you increase the decimal
Example:
Tokyo pop: x 107
Mexico City pop: x 106 = 1.56 x 107
Sao Paolo pop: x 108 = 1.65 x 107
NOW you can add them together and carry thru the exponent
Total= 5.91 x 107

20. Multiplying and Dividing using Scientific Notation
Multiplication:
Multiply decimals and ADD exponents
Ex : (1.2 x 106) x (3.0 x 104) = 3.6 x = 10
* Ex: (1.2 x 106) x (3.0 x 10-4) = 3.6 x (-4) = 2
Division:
Divide decimals and SUBTRACT exponents
Ex: (5.0 x 108) ÷ (2.5 x 104) = 2.0 x – 4 = 4
*Ex: (5.0 x 108) ÷ (2.5 x 10-4) = 2.0 x – (-4) = 12

21. Accuracy vs. Precision
Significant Figures

22. Accuracy and Precision
Accuracy: How close measurements are to the actual value Precision: How close measurements are to each other

23. Percent Error
An error is the difference between an experimental value and an accepted value
Percent error=
Percent error = accepted - experimental x 100
accepted value
A tolerance is a very narrow range of error

24. Example:
The accepted density for copper is 8.96g/mL. Calculate the percent error for each of these measurements.
8.86g/mL
8.92g/mL
9.00g/mL
8.98g/mL
[(8.96 – 8.86)/8.96] x 100% = 1.12%
[(8.96 – 8.92)/8.96] x 100% = 0.45%
[(9.00 – 8.96)/8.96] x 100% = 0.45%
[( )/8.96] x 100% = 0.22%

25. Significant Figures
Significant figures include all known digits plus one estimated digit
Rules
Non-zero numbers are always significant
Zeros between non-zero numbers are always significant (“trapped zeros”)
All final zeros to the right of the decimal place are significant (“trailing zeros”) (but trailing zeros don’t count if there is no decimal in the number)
Zeros that act as place holders are not significant (convert to SN to remove placeholder zeros) (“leading zeros”)
Counting numbers and defined constants have an infinite number of sig figs

26. Rounding numbers
An answer should have no more significant figures than the data with the fewest significant figures
Example:
Density of a given object = m = 22.44g = g/cm3
V cm3
How should the answer be rounded?
1.58 g/cm3

27. Addition & Subtraction
How do you add or subtract numbers that contain decimal point?
The easiest way (which you learned in third grade) is to line up the decimal points then perform the math
Then round according to the previous rule, rounding to the least numbers after the decimal! (ex: =  15.6)

28. Multiplication & Division
When you multiply or divide, your answer must have the same number of significant figures as the measurement with the fewest significant figures…just like adding or subtracting!
Ex: 38736km
4784km
=  8.097

29. Representing Data
A goal of many experiments is to discover whether a pattern exists in a certain situation…when data are listed in a table the patterns may not be obvious
Soooo, scientists often use graphs, which are visual displays of data
X-axis  independent variable
Y-axis  dependent variable