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Significant Significant Figures Figures The Four Rules The Four Rules
Significant FiguresSignificant FiguresSignificant FiguresSignificant Figures
The Four RulesThe Four Rules
Rule #1:All non-zero numbers are
always…
4 3
2
1
6
78
9
5
SIGNIFICANT!!!
So, the only number So, the only number to worry about is…to worry about is…
So, the only number So, the only number to worry about is…to worry about is…
0
Using Othello to understand Rule #2Zeros between non-zero numbers
are always significant
Using Othello to understand Rule #2Zeros between non-zero numbers
are always significant
The Other Zero Rules
All final zeros to the ______ of a decimal point are significant.
right
Zeros that act as ____________ are NOT significant.
placeholders
0.0000340000
Rule #3:
Rule #4:
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.
1000000.0
Significant?
Another note: if a number is Another note: if a number is written in scientific notation, written in scientific notation, all numbers all numbers beforebefore the x 10 the x 10 are significant, all numbers are significant, all numbers
afterafter are not significant. are not significant.
Another note: if a number is Another note: if a number is written in scientific notation, written in scientific notation, all numbers all numbers beforebefore the x 10 the x 10 are significant, all numbers are significant, all numbers
afterafter are not significant. are not significant.
Is ItIs ItSignificant?Significant?
Is ItIs ItSignificant?Significant?
16407.100
0.00010080
904008000
Significant Non-Significant
8 sig figs
5 sig figs
6 sig figs
Let’s look at some examples
a. 508.0 L
b. 820 400.0 L
c. 1.0200 x 105 kg
d. 807 000 kg
4 significant figures
7 significant figures
5 significant figures
3 significant figures
Let’s look at some examples
a. 0.049 450 s
b. 0.000 482 mL
c. 3.1587 x 10-8 g
d. 0.0084 mL
5 significant figures
3 significant figures
5 significant figures
2 significant figures
So, why are So, why are significant figures significant figures
important?important?
So, why are So, why are significant figures significant figures
important?important?
Significant figures and mathSignificant 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
189.903
189.9
961.95- 943
18.95
19
Multiplication and Division
• When multiplying or dividing—the product has the least number of significant figures
21.6x 0.067
1.4472
1.4
7216÷ 0.034
212235.294118
210000
(3 sig figs)
(2 sig figs)
(2 sig figs)
(2 sig figs)
(4 sig figs)
(2 sig figs)
Or 2.1 x 105
Now, try some of Now, try some of these on your ownthese on your ownNow, try some of Now, try some of
these on your ownthese on your own
Addition
a) 43.2 cm
51.0 cm
+ 48.7 cm
b) 258.3 kg
257.1 1 kg
+ 253 kg
c) 0.0487 mg
0.05834 mg
+ 0.00483 mg
142.9 cm 0.1 1 1 87 mg768.41 kg
768 kg 0.1119 mg
Multiplication
a) 24 m x 3.26 m
b) 120 m x 0.10 m
c) 1.23 m x 2.0 m
d) 53.0 m x 1.53 m
= 78.24 m
= 78 m
= 12 m
= 2.46 m= 81.09 m
= 2.5 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 Since the marks on this ruler are subdivided as ruler are subdivided as they are, our answer for they are, our answer for
the length of this nail has the length of this nail has 33 significant figures. significant figures.
Since the marks on this Since the marks on this ruler are subdivided as ruler are subdivided as they are, our answer for they are, our answer for
the length of this nail has the length of this nail has 33 significant figures. significant figures.
However, we only have However, we only have significant figures when significant figures when
we are we are measuringmeasuring something. something. CountingCounting will give you an exact will give you an exact
number.number.
However, we only have However, we only have significant figures when significant figures when
we are we are measuringmeasuring something. something. CountingCounting will give you an exact will give you an exact
number.number.
