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Significant Figures
All IB calculations must report answer to
correct # of sig fig’s.
All lab measurements must be reported to
correct sig fig’s and correct sig fig’s with
uncertainties must be reported properly.
• There are 2 kinds of
numbers:
–Exact: the amount of
money in your account.
Known with certainty.
–Approximate: weight,
height—anything
MEASURED. No
measurement is perfect.
When to use Significant figures
• When a measurement is
recorded only those digits that
are dependable are written
down.
What is this measurement?
1.35 cm
Measure the width of your
notebook paper in cm.
When to use Significant figures
–If you measured the
width of a paper with
your ruler you might
record 21.7cm.
To a mathematician 21.70,
or 21.700 is the same.
But, to a scientist 21.7cm and 21.70cm
is NOT the same
• 21.700cm to a scientist means
the measurement is accurate
to within one thousandth of a
cm.
But, to a scientist 21.7cm and
21.70cm is NOT the same
• If you used an ordinary ruler,
the smallest marking is the mm,
so your measurement has to be
recorded as 21.7cm*.
• *or 21.75 cm.
Reporting Sig Fig’s in measurement
Analog Instruments
• Use the smallest or half the smallest measure
on instrument. That will be the best you can
read. There will be situations where the
measure will be much less precise than that.
The smallest measure is 0.1 cm so
report 1.3 or 1.35 cm.
The last digit is an estimate.
Digital Instruments
• Use the place of the last digit at best.
1.00
1.00 V
How do I know how many Sig
Figs are in a reported number?
• All digits in the prefix before a power
of 10 are significant.
• 2.2 x 102
• 1.34 x 10 -2
• 4.0012 x 109.
How do I know how many Sig Figs
not in sci notation?
• All non-zero digits are signicant.
• All digits are significant starting
with the first non-zero digit on the
left.
• 0.0022 has 2 sig fig’s
• Exception to rule: In whole
numbers that end in zero,
the zeros at the end are not
significant.
100 Has 1 sig fig.
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
•
nd
2
Exception to rule: If zeros
are sandwiched between nonzero digits, the zeros become
significant.
1001
• 3rd Exception to rule: If zeros
are at the end of a number
that has a decimal, the zeros
are significant. They are there
to show precision.
3.000
• 3rd Exception to rule:
• These zeros are there to show
precision in the measurement
or calculation.
How many sig figs here?
•
•
•
•
•
•
1.2
2100
56.76
4.00
0.0792
7,083,000,000
•
•
•
•
•
•
2
2
4
3
3
4
How many sig figs here?
•
•
•
•
•
•
3401
2100
2100.0
5.00
0.00412
8,000,050,000
•
•
•
•
•
•
4
2
5
3
3
6
Rounding Rules
• If digit just past last sig fig is 5 or more
round up. If we need two sig fig’s,
• 3.67
3.7
5.55
5.6
• If digit past last sig fig is 4 or less drop
off last numbers:
3.322
3.3
What about calculations with sig figs?
• Rule: When adding or
subtracting measured numbers,
the answer can have no more
places after the decimal than the
LEAST of the measured
numbers.
Add/Subtract examples
• 2.45cm + 1.2cm = 3.65cm,
• Round off to
= 3.7cm
• 7.432cm + 2cm = 9.432
round to
 9cm
Multiplication and Division
• Rule: When multiplying or
dividing, the result can have
no more significant figures
than the least reliable
measurement.
A couple of examples
• 56.78 cm x 2.45cm = 139.111
• Round to
 139cm2
• 75.8cm x 9.6cm = ?
730 cm2.
2
cm
Practice with Sig Figs wksht
• Hwk Kerr pg 9 #2 – 12.