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.
Download
Report
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
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
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
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
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
In general: the more significant figures
you have, the more accurate the
measurement
Determining significant figures with
instrumentation
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
RULES FOR SIGNIFICANT
FIGURES
Rule 1: Nonzero digits are always significant
Rule 2: Zeros between nonzero digits are
significant
40.7 (3 sig figs.)
87009 (5 sig figs.)
Rule 3: Zeros in front of nonzero digits are
not significant
0.009587 (4 sig figs.)
0.0009 (1 sig figs.)
RULES FOR SIGNIFICANT
FIGURES
Rule 4: Zeros at the end of a number
and to the right of the decimal point
are significant
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)
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.
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:
You start with 998,567,000
Give this number in 3 sig figs.
ANSWER
Step 1: Get the first 3 numbers (3 sig figs.)
998
Step 2: Check to see if you have to round up
or keep the number the same
You need to look at the 4th number
9985
If the next number is 5 or higher, round up
If the next number is 4 or less, stays the same
Therefore = 999
ANSWER
Step 3: Look at your 3 numbers and
put them in scientific notation
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.)