October 20, 2011
Significant Figures
Significant Figures
Answers to Density/% error exercise
Abbreviated: Sig Figs
1. We are probably the reason for error. Ruler when compared to caliper.
Caliper gives last digit, ruler you guess.
Electronic scale when compared to triple beam balance (as long as error is .01
Why do we use Significant Figures?
g). The electronic scale that goes to .001 g would be more accurate.
Electronic scale can’t be calibrated to temp or pressure each day as can a
triple beam balance.
What are Significant Figures (Sig Figs)?
2. As said in class, there is no human error because lab partners do not write
down any measurement until both have made the measurement individually
and are with + 1 of the digit that is guessed. Human error is an excuse for
not doing what is expected.
3. Need as many measurements that assure that you are with + 1 of the digit
that is guessed. You may never take the average.
How many significant figures are there in the following:
(Remember these numbers represent measurements.)
How many significant figures are there in the following:
(Remember these numbers represent measurements.)
54
54
103
103
34.21
34.21
100
100
1206
1206
.00032
.00032
0.298
0.298
.00200
.00200
October 20, 2011
When are zeros significant?
Rounding:
In calculations always write out all digits on your calculator.
1. When between other numbers.
Choose by Significant Figure Rules how many digits may be kept in your
final answer.
Example: 3009
Round to that digit.
2. When after numbers that are after decimal points.
How do we "Round"
Example: 23.340
or
14.00
look to the right of the digit to be rounded: if a 0, 1, 2, 3, 4, round down.
3. When after decimal points after numbers.
look to the right of the digit to be rounded: if a 6, 7, 8, 9, round up.
Example: .00200
look to the right of the digit to be rounded:
if a 5 consider the "Stupid Rule"
4. When written in scientific notation.
Example: 2.00 x 10
-3
Stupid Rule:
If after the 5 there no numbers or only O(s), then round the digit to
be rounded to the EVEN number.
Digits
Consider the number 1 meter.
If after the 5 there are numbers, then round the digit to be rounded,
up.
.001 km = 1 meter = 100 cm = 1000 mm
How many sig figs are in each number?
examples:
4.50000 rounded to one significant figure = 4
3.500 rounded to one significant figure = 4
4.2567 rounded to two significant figures = 4.3
4.2500 rounded to two significant figures = 4.2
So when you get a 12.5 on a lab report out of 15 points possible, and
the grade program does not recognize decimals, your score would be
a 12. Students often say that this is a ____________ Rule.
So a conversion can not change the accuracy or the number of
Significant Figures.
Zeros are used to "hold space", do not count.
October 20, 2011
Problem
Scientific Notation:
Definition: A single digit (1-9), decimal point, followed by all significant
numbers times 10 to an exponent.
Example 1000,
with + 10 error
= 1.00 x 103
"Regular"
(one digit)
"Stupid"
(one digit)
4.0
4.5
4.5
5.0
3.0
3.5
3.5
2.0
4.0
34.0
Addition and Subtraction
Addition and Subtraction
Answer must show the "worst" error of any of the measurements.
3
Example
3
Example
+1
7
+1
4
+1
20
7
+1
10010
10010
+
10.00
1.0 x 103
+ 1.45 x 102
+
151
_
151
_
4
+1
+
+1
+
Answer must show the "worst" error of any of the measurements.
10.00
20
1.0 x 103
+ 1.45 x 102
October 20, 2011
Image addition problems
Image addition problems
October 20, 2011
Image measurements B
Multiplication / Division rules are different than Addition / Subtraction rules.
To determine the correct error and significant digits in a computation involving
multiplication and division, go by the least significant digits given in any of the
measurements.
Example:
3
one significant digit
4
one significant digit
x
12
Example:
can only have one significant digit to match with the one
from both measurements. Thus the answer rounded to
one significant digit would be 10.
2 x 20. = 40
(2 has one sig fig., 20 has two sig figs., by the rule, may only keep one sig fig.
in answer. 40 has only one sig fig and represents + 10 error)
multiplication sig figs
October 20, 2011
Multiplication / Division Practice
practice sig figs
sig figs mult
Multiplication / Division Practice
October 20, 2011