1. Measurement
Numbers are very important in science and the way in which scientists interpret them must be uniform. In other words, all scientists must be speaking the same language so they can understand one another.
In science a procedure called peer review is utilized. In this process an individual does an experiment and wants to give the information to the science community. She/he publishes it in a scientific journal so other scientists can look at their work. Some scientists then try to repeat the experiment and see if they can produce the same results. This insures that people have not made mistakes or lied about their research.

2. Data
Therefore when numbers are used as data (quantitative data) we must understand what we mean by them.
The numbers we use are from experiments in which we measure things.
Some things can be measured exactly while others cannot.
People can be measured exactly because it is done one by one. However, other things like the length of a piece of paper cannot be measured exactly.
Your measurement depends on how precise your instrument is.

3. One of the rulers above (when measuring in inches) is more precise
One of the rulers above (when measuring in inches) is more precise. Which one and why?
Why is this important?

4. Sig Fig Rules
There are a few rules we will learn to determine the number of significant figures in a number:
Numbers for data that are counted one by one have INFINITE significant figures.
All numbers 1-9 are significant
Zero’s are significant EXCEPT when:
Trailing zeros: The number is greater than 1, there is no decimal and they are at the end of a number.
EX: 3,000 (The last 3 zero’s are NOT significant)
EX: 3,000. (These zeros ARE significant)
Leading Zeros: The number is less than 1 and they appear at the front of a number.
EX: (The first 4 zeros are NOT significant)
EX: (The first 4 zeros are NOT significant but the last two ARE.)
Middle zeros: Zeros in between to significant digits are always significant.
EX: (the middle zero is significant but the last one is not)
EX: (the leading zeros are not significant but the middle and trailing zeros are)

5. Practice Time
State the number of significant numbers in each set: = ____ = ____ = ____ = ____ = ____ = ____ 7. 2,000,000= ____ = ____ = ____ = ____ ,000 = ____ ,030 = ____ 13. 8,000. = ____ ,200 = ____ = ____ = ____ = ____ = ____ = ____ ,000 = ____ = ____ = ____ = ____ = ____

6. Scientific Notation
Instead of using standard notation scientists write numbers in scientific notation. This system uses the base 10 as a multiplying factor to move the decimal place around.
X 100 = times 1
X 101 = times 10 X 10-1 = times .1
X 102 = times X 10-2 = times .01
And so on……. The base 10 moves the decimal around. So why do we use this? The answer is simple. In science we commonly have to use numbers that are very large or very small and scientific notation is easier to use than standard notation. For example the number of atoms in grams (1mole) of carbon is:
602,000,000,000,000,000,000,000
This would be a pain to write so instead we use: 6.02 X 1023

7. Sci. Not. Rules So how do we do this? Here are some general rules:
The decimal place should be moved to the right of the first non-zero number.
The number in front of the base 10 needs to be a number 1 – 10.
The number of times you move the decimal becomes the superscript of the base 10. Positive if the number is greater than zero and negative if less than zero.
NOTE: Only significant numbers are included in scientific notation.

8. Convert the standard notation into scientific (watch your sig figs)
,000 = ___________2. 8,000. = ____________
= ___________ ,001 = ____________
= ____________ = ____________
= ___________ = ____________
= ____________ = ____________

9. Convert the scientific notation to standard (watch your sig figs)
6.02 X 10-4 = ____________________
2.02 X 10-8 = ____________________
2.00 X 10-5 = ____________________
X = ______________________
9 X 100 = _______________________
X 106 = ___________________
3.0 X 105 = _____________________
X 106 = _______________________
5.000 X 101 = ___________________
X 102 = _____________________

10. Rounding What is rounding? 1) 15.6 (2) 2) 15.6 (1) 3) 690 (1)
It comes from the idea that some numbers are irrelevant or not significant and therefore not reliable.
In science, we do not round like math. We must round to the appropriate number of sig figs.
1) (2)
2) (1)
3) 690 (1)
4) 5,555 (2)
5) 8.12 X 104 (2)
6) 9.5 X 102 (1)
7) 4.5 X 104 (1)

11. Round the value to the number of Sig. Figs
Round the value to the number of Sig. Figs. indicated by the parenthesis.
555.5 (1)______ (4)______ (1)_______
(2)______ (1)________ (1)______
(3)______ ,500. (4)______ (1)_____
(1)______ (1)________ (1)_____
995. (2)________ ,500 (3)______
(4)_______

12. Sig Fig Calculations
As has been discussed, numbers are very important and their reliability is crucial when using them for practical applications.
When doing science we often take the data that we have measured and manipulate it to find a multitude of other information.
In other words, we take the numbers from our experiment and we will add, multiply, subtract, and divide them in order to calculate other derived quantities.
However, the problem arises in that all numbers are NOT created equally.

13. Addition & Subtraction
Look at all the numbers that are in your calculation and determine which has the least number of decimal places. Your answer should have the same number of decimal places as this one. (Units must be the same)
EX: g +12.5g g = Final answer rounded = 39.1g

14. Multiplication & Division
Look at all the numbers that are in your calculation and determine which has the least amount of significant figures. Your answer should have the same number of significant figures as this one.
Treat units like variables in algebra
EX: ,000. m3 = m = 3.0 X 102 m
10. m2
EX:( ft) X (11ft) = ft2 = 130 ft2

15. Calculation Practice
g5/6g = ___________________2. (5500m-9)(56.m) = _________________
nm+ 8.3 nm – 30.0 nm = _____ g L L– 226 =_____
5. (60.0g)/(230 cm3) g/cm3 = ______6. (0.020ml)( ml) + 1 ml2 =___
X 107 nm3 / 4.00 X 107 nm = _______ 8. (1 X 107 kg3)(2.45 X 10-4 ft-3) = ___
X 102 ml X 103 ml4 = _______ X 10-2 ft X 10-3 ft-3 = ____
11. (6.9 X 107 Kg3 / 4.00 X 106 Kg3) - 8 X 101 kg- 2.3 X 101 kg3________________