Scientific Notation and Significant Digits

today is sept 23rd and this is our second official post and my first blog post ever! today we learned about scientific notation( SN) and significant digits(SD).Yay math! basically precision and accuracy are super important in chem so we need to make sure that we write numbers properly and only write the numbers that are important.
SDs
first lets talk about significant digits or SD. significant digits are digits that actually matter in a number
there are 3 rules for finding significant digits.

1.Non zero numbers are always significant
2. If a zero is a placeholder, it it generally not significant
3. If a number is to the right of a non-zero number, it is generally significant

ex. 0.000056 has 2 SDs5 and 6
      but 0.9000070005 has 10 SDs
a good way to find SDs is to find the first number and count to the right untill you run out of numbers: 2.0000 has 5 SDs

when you add or subtract SDs always round to the least precise number
ex. 7.4212-3.54= 3.8812 becomes 3.88
when you mulyiply or divide SDs round to the number with the fewest SDs
ex. 2.5*5.5= 13.875 becomes 14

SN
so scientific notation is making a long number like this: 1230000000000000000, into a shorter, easier to write number like this: 1.23 * 1018. its the same number but it takes up way less room.
here are some more examples


MULTIPLYING AND DIVIDING SN

when you multiply or divide SN numbers things get a little more complicated.
ex. multiplying


the answer would be 9 because you have to multiply 2 and 4 together and add the exponents together.

ex. dividing


so you divide the numbers (8.03 and 5.25) and then subtract the exponents

ADDING AND SUBTRACTING IN SN

adding and subtracting are also complicated because you have to make the exponents of both the numbers the same before you add or subtract. this depends on the exponents of each expression.
ex     5.3*104  plus  2.3*103
in this case you have to make the exponents the same so 2.3 would be changed to .23*104
then you can add them together to get 5.53*104
the problem here is that the precision has in creased so you have to take away 2 digits to get
                                                                                 5.5*104
the process is the same with subtraction except you subtract the numbers

this is a link to a video that explains everything that i have on here but with diagrams and such so if you are interested check it out
http://www.youtube.com/watch?v=l3Dv8fV12FA&feature=related