Transcript Uncertainty in Measurement and Significant Figures

Chapter 5, Section 2
 Every
measurement device has its
limitations
 You can only estimate between points,
but not beyond
 Example: a bathroom scale doesn’t give
your weight to the thousandth of a pound
A
beaker is never an accurate measurement
device.
 For accurate liquid measurement, use a
graduated cylinder
 The liquid in a graduated cylinder may for a
curve, called a meniscus
 When reading a graduated cylinder, always
read the bottom of the meniscus
 Significant
figures are numbers recorded
in a measurement. This includes certain
digits and the first uncertain digit in the
measurement.
 You will often see significant figures
abbreviated as “sig figs”
 Sig figs determine the maximum amount
of numbers you can use in an answer
Nonzero integers always count as significant
figures. Ex: 1457 is all no zero integers, so all
count as sig figs
Zeros fall into three groups:
1.
2.
1.
2.
3.
3.
Leading zeros are zeros that preceded nonzero
digits. They NEVER count as sig figs
Captive zeros are zeros that fall between nonzero
digits. They ALWAYS count as sig figs
Trailing zeros are zeros at the right end of the
number. They are only significant when written
with a decimal point.
Exact numbers, like numbers obtained by
counting, will never limit the number of sig figs
in a calculation
 How
many significant figures do the following
numbers have?
 0.0108 g of vitamin C

3 sig figs; the leading zeros don’t count, but the
captive zero does
 480

cars
3 sig figs; this is an exact number
 5.030

x 103 ft
4 sig figs; both zeros are significant
 0.00100

m
3 sig figs; the leading zeros don’t count, but the
trailing zeros do
 When
you perform a calculation on your
calculator, the number displayed is usually
greater than the number of sig figs
 You must “round off” your calculations so
your answer equals the correct number of sig
figs allowed
If the digits to be removed…
1.
1.
2.
2.
Is less than 5, the preceding digit stays the
same
Is equal to or greater than 5, the preceding
digit is increased by 1.
In a series of calculations, carry the extra
digits to the end and then round off. Do
not round off at each step.
 For
multiplication and division, significant
figures are counted.

Use the smallest number of sig figs in your answer
 For
addition and subtraction, the decimal
places are counted

Use the smallest number of decimal places in your
answer
 Multiplication




4.56 x 1.4 = 6.384
4.56 = 3 sig figs; 1.4 = 2 sig figs
Answer needs 2 sig figs
Rounding off answer = 6.4
 Division




Example:
Example
8.315/298 = 0.0279027
8.315 = 4 sig figs; 298 = 3 sig figs
Answers needs 3 sig figs
Rounding off answer = 2.79 x 10-2
 Addition




Example
12.11 + 18.0 + 1.013 = 31.123
12.11 = 2 decimals; 18.0 = 1 decimal; 1.013 = 3
decimals
Answer must have only 1 decimal
Rounding off Answer = 31.1
 Subtraction




Example
0.6875 – 0.1 = 0.5875
0.6875 = 4 decimals; 0.1 = 1 decimal
Answer must have only 1 decimal
Rounding off Answer = 0.6