Scientific Notation and Significant Figures

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

Going from standard number form to scientific notation 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 = 3.1 x Now try some!!!

Math with 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 x 10 3 = 5.4 x 10 3 Now try some!!!

Exceptions 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!!!

Multiplying and Dividing 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

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”

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

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

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

Math with Sig Figs Adding/Subtracting ◦Answer should have the same number of DECIMAL PLACES as the original number with the LEAST amount of decimal places  Example: = 3.42

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 ◦ x 2.00 = 28 = 28.0 ◦ 45,000 x 112 = 5,040,000  5.0 x 10 6