Download 1021488Notes Sig Figs

Calibration vs. Precision
• If a balance is accurate, it should read 0
when nothing is on it.
• The process for making sure a balance or
any equipment is accurate is called
CALIBRATION.
• Clocks can measure to the minute, second
or fraction of a second.
• This refers to an instrument’s PRECISION.
Need for Sig Figs
• Measurements must reflect the precision
of the instrument used, so significant
figures become important.
• When measuring, you record all known
digits plus you estimate the final digit if
possible.
• For example if your ruler measures to the
nearest cm, you would estimate how far it
is between the 2 cm markings.
Rules for counting sig figs
1. All nonzero numbers ARE significant
Ex: 234.5 = 4 sig figs
2. All zeros between nonzero numbers ARE
significant
Ex: 2304.5 = 5 sig figs
Rules for counting sig figs
3. Zeros that act as placeholders ARE NOT significant.
Think of how you’d rewrite these numbers as a
fraction or in scientific notation – the zeros would
disappear.
This includes any zeros left of nonzero digits or any
number ending in zero that does NOT include a
decimal.
Ex: 0.0234 = 3 sig figs
14320 = 4 sig figs
Rules for counting sig figs
4. All final zeros to the right of the decimal
are significant.
Ex: 23.00 = 4 sig figs
5. Counting numbers and defined constants
have an infinite number of sig figs.
Ex: 6 molecules, 60 seconds in a minute
or 100%
Try It
• Round each figure to 3 sig figs:
219034
25.38
0.08763
119.99
Solutions
• Round each figure to 3 sig figs:
219034 = 219,000
25.38 = 25.4
0.08763 = 0.0876
119.99 = 120.
Counting Sig Figs when
adding/subtracting
• Your final answer must have the same
number of sig figs to the right of the
decimal as the starting value with the
fewest digits to the right of the decimal.
Ex: 2.54 + 3.1 + 2.275 = 7.915 BUT your
final answer needs to round to 7.9
Counting Sig Figs when
multiplying/dividing
• Your final answer must have the same
number of sig figs as the starting value
with the fewest significant figures.
Ex: A box measures 2.5 on a side, so you
find the volume to be 15.625 BUT you
must round your answer to 16 cm3 since
you only had 2 sig figs in your
measurement.
Try It
• Complete the following problems, rounding
answers to the correct number of sig figs:
(5.53 x 10-6 km) x (7.64 x 103 km)
(9.33 x 104 mm) / (3.0 x 102 mm)
(4.42 x 10-3kg) – (2.0 x 102 kg)
Solutions
• Complete the following problems, rounding
answers to the correct number of sig figs:
(5.53 x 10-6 km) x (7.64 x 103 km)
= 4.22 x 10-2 km
(9.33 x 104 mm) / (3.0 x 102 mm)
= 3.1 x 102
(4.42 x 10-3kg) – (2.0 x 102 kg)
= -2.0 x 102
Try It
• The accepted length of a steel pipe is 5.5
m. Calculate the percent error and round
to the correct number of sig figs for these
measurements:
5.7 m
5.1 m
Try It
• The accepted length of a steel pipe is 5.5
m. Calculate the percent error and round
to the correct number of sig figs for these
measurements:
5.7 m = .2/5.5 x 100% = 3.6%
5.1 m = -.4/5.5 x 100% = -7.3%