Transcript Significant figure

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
more significant figures), the closer you
get to the true value.
 How
do we determine how many
significant figures are in different pieces of
lab equipment?
SIGNIFICANT FIGURES
 Significant
figure – any digit in a
measurement that is known for sure plus
one final digit, which is an estimate
 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
 Try
these:
Graduated
cylinder
Triple Beam balance
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: Take your numbers and put the
decimal after the first digit

9.99
 Step
4: Count the number of places you
have to move to get to the end of the
number and put it in scientific notation.

9.99 x 108
 NOTE:
If the number is BIG it will be a
positive exponent. If the number is a
DECIMAL, it will be a negative exponent.
OTHER POSSIBILITY
 Example:


999,999,999 (3 sig. figs.)
When you take the first three numbers, you
get
 999


But when you round, it is going to round
from 999  1000
Therefore, the number becomes:
 1.00
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.)