Transcript Scientific Notation and Significant Figures

Scientific Notation and
Significant Figures
◦ A positive exponent means move the decimal
to the right
 Ex. 1.34 x 104 = 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 104
◦ 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 103 + 2.1 x 103 = 5.4 x 103
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
oExample: 7.1 x 104 – 2.0 x 103
o7.1 x 104 can become 71 x 103
o2.0 x 103 can become .2 x 104
Now try some!!!
Exceptions

Multiplying
◦ When multiplying numbers in scientific
notation, the exponents are added
 Ex. 3.0 x 103 * 2.0 x 104 = 6.0 x 107

Dividing
◦ When dividing numbers in scientific notation,
the exponents are subtracted
 Ex. 9.0 x 105 / 3.0 x 102 = 3.0 x 103
 Ex. 3.0 x 103 / 2.0 x 104 = 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 = 3.42
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
◦ 14.000 x 2.00 = 28 = 28.0
◦ 45,000 x 112 = 5,040,000  5.0 x 106
Math with Sig figs