Transcript Significant Figure Rules

Significant Figure Rules
1
4 Rules to determine how many
significant figures are in a number:
1. Non-zero digits are always significant.
2. Zeros between two numbers are
significant.
3. Zeros to the left of the number are never
significant
4. Zeros to the right of a number are only
significant if there is a decimal point.
2
Something to think about…
Because all measurements are uncertain, we
must only use those numbers that are
meaningful.
A common ruler cannot measure something to
be 22.4072643 cm long. Not all of the digits
have meaning (significance), and therefore
should not be written down.
In science, only the numbers that have
significance (derived from measurement) are
written.
3
Rule 1: Non-zero digits are always
significant.
If you measure something and the device you use
(ruler, thermometer, triple-beam balance, etc.)
returns a number to you, then you have made a
measurement decision and that ACT of measuring
gives significance to that particular numeral (or
digit) in the overall value you obtain.
Ex: 26.38 = 4 sig. figures
Ex: 7.94 = 3 sig. figures.
THE PROBLEM: numbers such as 0.00980 or
28.09.
4
Rule 2: Any zeros between two
numbers are significant.
Ex: 406
By the first rule, the 4 and 6 are significant.
However, to make a measurement decision
on the 4 (in the hundred’s place) and the 6
(in the unit’s place), you HAD to have made
a decision on the ten’s place.
5
Rule 3: Zeros to the left of the
number are never significant
Space holding zeros on numbers less than one.


0.00500
0.03040
These zeros serve only as space holders. They
are there to put the decimal point in its correct
location. They do NOT involve measurement
decisions.
When you write them in scientific notation (5.00
x 10-3 and 3.040 x 10-2), the non-significant
zeros disappear!
6
Rule 4: Zeros to the right of a number are
only significant if there is a decimal point.
This rule causes the most difficulty.
Here are two examples of this rule with the zeros
this rule affects in red:
0.00500
0.03040
Here are two more examples where the
significant zeros are in red:
2.30 x 10-5
4.500 x 1012
7
Rule 4: Zeros to the right of a number are
only significant if there is a decimal point.
200 is considered to have only ONE significant
figure while 25,000 has two.
This is based on the way each number is written.
When whole numbers are written as above, the
zeros, BY DEFINITION, did not require a
measurement decision, and so they are not
significant.
If you want 200 to have 2 sig. figures, write it in
scientific notation: 2.0 x 102
For 3 sig. figures, write 2.00 x 102 or with a
decimal at the end: 200.
8
Infinite Significance
Numbers that are not measured are
considered to have infinite significance
Counting numbers



36 cars
50 people
200,000,000 grains of sand
Definitions


1 m = 1000 mm
The boiling point of water is 100°C
9
Some Practice:
How many significant
digits are there in each of
the following quantities?
Why?
Answers
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
20 kg
0.0051 g
11 m
0.010 s
90.4 degrees Celsius
0.004 cm
0.089 kg
0.009 00 L
100.0 degrees Celsius
20 cars
1
2
2
2
3
1
2
3
4
infinite
10