Transcript SIGNIFICANT FIGURES ACCURACY VS. PRECISION   In labs, we are concerned by how “correct” our measurements are They can be accurate and precise   Accurate: How close.

SIGNIFICANT FIGURES
ACCURACY VS. PRECISION


In labs, we are concerned by how
“correct” our measurements are
They can be accurate and precise


Accurate: How close a measured value is
to the actual measurement
Precise: How close a series of
measurements are to each other
EXAMPLE
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
The true value of a measurement is
23.255 mL
Below are a 2 sets of data. Which one
is precise and which is accurate?
1.
2.
23.300, 23.275, 23.235
22.986, 22.987, 22.987
SCIENTIFIC INSTRUMENTS

In lab, we want our measurements to
be as precise and accurate as possible
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For precision, we make sure we calibrate
equipment and take careful measurements
For accuracy, we need a way to determine
how close our instrument can get to the
actual value
SIGNFICANT FIGURES
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We need significant figures to tell us how
accurate our measurements are
The more accurate, the closer to the actual
value
Look at this data. Which is more accurate?
Why?
 25 cm
 25.2 cm
 25.22 cm
ANSWER
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
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25.22cm
The more numbers past the decimal,
the closer you get to the true value.
How do we determine how many sig.
figs. we have?
SIGNIFICANT FIGURES


Significant figure – any digit in a
measurement that is known with certainty
plus one final digit, which is uncertain
Example:
 4.12 cm
 This number has 3 significant figures
 The 4 and 1 are known for certain
 The 2 is an estimate
SIGNIFICANT FIGURES
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In general: the more significant figures
you have, the more accurate the
measurement
Determining significant figures with
instrumentation
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Find the mark for the known
measurements
Estimate the last number between marks
SIGNIFICANT FIGURES

Let’s look at some examples:
Graduated cylinder
 Meter stick
 At your desk:
 Ruler
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RULES FOR SIGNIFICANT
FIGURES
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Rule 1: Nonzero digits are always significant
Rule 2: Zeros between nonzero digits are
significant
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40.7 (3 sig figs.)
87009 (5 sig figs.)
Rule 3: Zeros in front of nonzero digits are
not significant
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0.009587 (4 sig figs.)
0.0009 (1 sig figs.)
RULES FOR SIGNIFICANT
FIGURES
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Rule 4: Zeros at the end of a number
and to the right of the decimal point
are significant
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85.00 (4 sig figs.)
9.070000000 (10 sig figs.)
Rule 5: Zeros at the end of a number
are not significant if there is no decimal

40,000,000 (1 sig fig)
RULES FOR SIGNIFICANT
FIGURES

Rule 6: When looking at numbers in scientific
notation, only look at the number part (not
the exponent part)

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3.33 x 10-5 (3 sig fig)
4 x 108 (1 sig fig)
Rule 7: When converting from one unit to
the next keep the same number of sig. figs.

3.5 km (2 sig figs.) = 3.5 x 103 m (2 sig figs.)
HOW MANY SIGNIFICANT
FIGURES?
1.
35.02
2.
0.0900
3.
20.00
4.
3.02 X 104
5.
4000
ANSWERS
1.
4
2.
3
3.
4
4.
3
5.
1
ROUNDING TO THE CORRECT
NUMBER OF SIG FIGS.
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Many times, you need to put a number
into the correct number of sig figs.
This means you will have to round the
number
EXAMPLE:
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You start with 998,567,000
Give this number in 3 sig figs.
ANSWER
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Step 1: Get the first 3 numbers (3 sig figs.)
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998
Step 2: Check to see if you have to round up
or keep the number the same
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You need to look at the 4th number
9985
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If the next number is 5 or higher, round up
If the next number is 4 or less, stays the same
Therefore = 999
ANSWER
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Step 3: Look at your 3 numbers and
put them in scientific notation
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9.99
Step 4: Count the number of places
you have to move the decimal to get
the exponent

9.99 x 108
TRY THESE
1.
2.
3.
4.
5.
10,000 (3 sig. figs.)
0.00003231 (2 sig. figs.)
347,504,221 (3 sig. figs.)
0.000003 (2 sig. figs.)
89,165,987 (3 sig. figs.)