◦ A positive exponent means move the decimal to the right
 Ex. 1.34 x 10 4 = 13,400
◦ A negative exponent means move the decimal to the left
 Ex. 5.12 x 10 -2 = 0.0512
Now try some!!
Going from scientific notation to standard number form.


Numbers in scientific notation should begin with a number between 1 and 10 and then should be followed by “x 10” with an exponent.
◦ Large numbers will have a positive exponent
 Ex. 67,000 = 6.7 x 10 4
◦ Small numbers will have a negative exponent
 Ex. 0.000031 = 3.1 x 10 -5
Now try some!!!
Going from standard number form to scientific notation


Adding/Subtracting Rules
◦ Numbers must have the SAME exponent
◦ Then, just add the numbers as normal and keep the original exponent
 Ex. 3.3 x 10 3 + 2.1 x 10 3 = 5.4 x 10 3
Now try some!!!
Math with scientific notation!

What if they are not the same??
o
If exponents are not the same, one must be adjusted o Example: 7.1 x 10 4 – 2.0 x 10 3 o 7.1 x 10 4 can become 71 x 10 3 o 2.0 x 10 3 can become .2 x 10 4
Now try some!!!
Exceptions


Multiplying
◦ When multiplying numbers in scientific notation, the exponents are added
 Ex. 3.0 x 10 3 * 2.0 x 10 4 = 6.0 x 10 7

Dividing
◦ When dividing numbers in scientific notation, the exponents are subtracted
 Ex. 9.0 x 10 5 / 3.0 x 10 2 = 3.0 x 10 3
 Ex. 3.0 x 10 3 / 2.0 x 10 4 = 1.5 x 10 -1
Multiplying and Dividing

Significant Figures

When rounding, we make certain numbers
“insignificant” therefore there are rules with respect to which numbers matter in chemistry

These are called “sig figs”


All non-zeros ARE significant
◦ Examples: 1.23 has three sig figs
41.12 has four sig figs

Zeros between non-zeros ARE significant
◦ Examples: 1205 has four sig figs
1.3021 has five sig figs
The Rules


Placeholder zeros are NOT significant
◦ Examples: 34,000 has two sig figs
0.0002 has one sig fig but…. 34,001 has five sig figs… why?

Final zeros after a decimal ARE significant
◦ Examples: 1.200 has four sig figs
34,000.00 has seven sig figs
The Rules


How many sig figs do the following have?
◦ 3.002
◦ 12,000
◦ 12,000.00
◦ 0.009
◦ 12
Now try some!!!
Practice!!


Adding/Subtracting
◦ Answer should have the same number of
DECIMAL PLACES as the original number with the LEAST amount of decimal places
 Example: 1.12 + 2.3 = 3.4
2
Math with Sig Figs


Multiplying/Dividing
◦ Answer should have the same number of SIG
FIGS as the original number with the LEAST amount of sig figs.
 Examples:
◦ 3.40 x 1.2 = 4.08  4.1
◦ 7 x 24 = 168  200
◦ 14.000 x 2.00 = 28 = 28.0
◦ 45,000 x 112 = 5,040,000  5.0 x 10 6
Math with Sig figs