Significant Figures
Unit 1 Presentation 3
Scientific Notation
The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
0.0000000000000000000000199
1.99 x 10-23
N x 10n
N is a number
between 1 and 10
n is a positive or
negative integer
Scientific Notation
568.762
0.00000772
move decimal left
move decimal right
n>0
n<0
568.762 = 5.68762 x 102
0.00000772 = 7.72 x 10-6
Addition or Subtraction
1. Write each quantity with
the same exponent n
2. Combine N1 and N2
3. The exponent, n, remains
the same
4.31 x 104 + 3.9 x 103 =
Scientific Notation
Multiplication
1. Multiply N1 and N2
2. Add exponents n1 and n2
Division
1. Divide N1 and N2
2. Subtract exponents n1 and n2
(4.0 x 10-5) x (7.0 x 103) =
8.5 x 104 ÷ 5.0 x 109 =
Significant figures (sig figs)
How many numbers in a measurement mean
something
When we measure something, we can (and do)
always estimate between the smallest marks.
1
2
3
4
5
Significant figures (sig figs)
The more marks the better we can
estimate.
Scientists understand that the last number
measured is actually an estimate
1
2
3
4
5
Sig Figs
What is the smallest mark on the ruler that
measures 142.15 cm?
142 cm?
140 cm?
Here there’s a problem: Does the zero count
or not?
Scientists needed a set of rules to decide
which zeroes count.
All other numbers always count
Which zeros count?
Leading zeros never count
– 0.045
Trapped zeros always count
– 100365405.057
Trailing zeros only count if there is a
decimal place present
– 12400
– 12400.
Here the zeroes do NOT count
Here the zeroes DO count
Sig Figs
Only measurements have sig figs.
Counted numbers are always exact
– A dozen is exactly 12
A a piece of paper is measured 11 inches
tall.
Being able to locate, and count significant
figures is an important skill.
Sig figs.
Count the sig figs and the number of significant
zeros in the following numbers
–
–
–
–
–
–
458 g
4085 g
4850 g
0.0485 g
0.004085 g
40.004085 g
Adding and subtracting with
significant figures
The last significant figure in a
measurement is an estimate.
Your answer can not be better (more
precise) than your worst (least-precise)
estimate.
You have to round it to the least place of
precision of the measurement in the
problem
For example
27.93 + 6.4

+
First line up the decimal places
Then do the adding
27.93
Find the estimated
6.4
numbers in the problem
34.33 This answer must be
rounded to the tenths place
Practice
4.8 + 6.8765
520 + 94.98
0.0045 + 2.113
6.0 x 102 - 3.8 x 103
5.4 - 3.28
6.7 - .542
500 -126
6.0 x 10-2 - 3.8 x 10-3
Multiplication and Division
Rule is simpler
Answer will have the same number of sig figs as
the value with the least number of sig figs in
the problem
3.6 x 653 = 2350.8
3.6 has 2 s.f. 653 has 3 s.f.
answer can only have 2 s.f.
2400
Note that there is NO decimal point present!
Multiplication and Division
Same rules for division
Lets do some practice.
4.5 / 6.245
4.5 x 6.245
9.8764 x .043
3.876 / 1983
16547 / 714