Transcript All non-zero numbers are always…

Significant Figures
The Four Rules
Rule #1:
All non-zero numbers are always…
SIGNIFICANT!!!
4
6
9
3
2
7
1
8
5
So, the only number to
worry about is…
0
Using Othello to understand Rule #2
Zeros between non-zero numbers
are always significant
Using Othello to understand Rule #2
Zeros between non-zero numbers
are always significant
The Other Zero Rules
Rule #3:
All final zeros to the ______
right of a
decimal point are significant.
0.0000340000
Rule #4:
Zeros that act as ____________
placeholders are
NOT significant.
For rule #3 and #4, it can be
summarized by these two questions:
1) Is there a decimal point?
2) Is there a number in front of the
zero?
Answering yes to both of these
questions means that the zeros are
significant figures.
Significant?
1000000.0
Another note: if a number is
written in scientific notation,
all numbers before the x 10
are significant, all numbers
after are not significant.
Is It
Significant?
Significant
Non-Significant
16407.100
0.00010080
904008000
8 sig figs
5 sig figs
6 sig figs
Let’s look at some
examples
a. 508.0 L
b. 820 400.0 L
4 significant figures
7 significant figures
c. 1.0200 x 105 kg 5 significant figures
d. 807 000 kg
3 significant figures
Let’s look at some
examples
a. 0.049 450 s
b. 0.000 482 mL
5 significant figures
3 significant figures
c. 3.1587 x 10-8 g 5 significant figures
d. 0.0084 mL
2 significant figures
So, why are significant
figures important?
Significant figures and math
Addition and Subtraction
• When adding or subtracting—the answer
has the least number of decimal places
• Hint: Before adding and subtracting, line
up all the numbers so the decimal points
align.
187.6
+ 2.303
961.95
- 943
189.903
18.95
189.9
19
Multiplication and Division
• When multiplying or dividing—the
product has the least number of
significant figures
21.6
x 0.067
1.4472
1.4
(3 sig figs)
(2 sig figs)
(2 sig figs)
7216
÷ 0.034
(4 sig figs)
(2 sig figs)
212235.294118
(2 sig figs)
210000
Or 2.1 x 105
Now, try some of these
on your own
Addition
a) 43.2 cm
51.0 cm
+ 48.7 cm
142.9 cm
b) 258.3
kg
257.1 1 kg
+ 253
768.41
kg
kg
768 kg
c) 0.0487
mg
0.05834 mg
+ 0.00483 mg
0.1 1 187 mg
0.1119 mg
Multiplication
a) 24 m x 3.26 m
= 78.24 m = 78 m
b) 120 m x 0.10 m
= 12 m
c) 1.23 m x 2.0 m
= 2.46 m = 2.5 m
d) 53.0 m x 1.53 m
= 81.09 m = 81.1 m
Why do we have them?
When we measure things, we want to
measure to the place we are sure of and
guess one more space.
So, they show the uncertainty
in our measurements
Since the marks on this
ruler are subdivided as they
are, our answer for the
length of this nail has 3
significant figures.
However, we only have
significant figures when
we are measuring
something. Counting will
give you an exact number.