Transcript Significant Figures

Significant Figures
Measured Numbers
When you use a
measuring tool is used to
determine a quantity
such as your height or
weight, the numbers you
obtain are called
measured numbers.
Exact Numbers
Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools
Exact numbers are obtained by
1.
2.
3.
4.
Counting
Definition
Measuring
Counting &
Definition
Measured numbers are obtained by
1. Measuring
2. Counting
3. Definition
Classify as exact or measured
number : Gold melts at 1064
Celsius.
1. Exact
2. Measured
Classify as exact or measured:
1 yard = 3 feet
1. Exact
2. Measured
Classify as exact or measured:
A red blood cell with diameter 6 x
10 -4cm.
1. Exact
2. Measured
Classify as exact or measured:
There were six hats on the shelf.
1. Exact
2. Measured
Classify as exact or measured:
A can of soda contains 355 mL of
soda.
1. Exact
2. Measured
Uncertainty in Measurement
The numbers reported in a
measurement are limited by the
measuring tool
Significant figures in a measurement
include the known digits plus one
estimated, or uncertain digit
This nail is 6.3
centimeters long for
sure, but what exactly
is the value of the
hundredths place
– 6.35, 6.36, 6.37?
“Significant figures in a measurement
consist of all the digits known with
certainty plus one final digit, which is
somewhat uncertain or is estimated.”
In the nail example, the hundredths place
(3.36, the 6) is uncertain, or estimated.
A SIGNIFICANT FIGURE IS NOT ALWAYS
CERTAIN – THE LAST DIGIT OF ANY
MEASUREMENT IS ESTIMATED!!!
Rules For Significant Figures
1) All non-zero digits are significant
Examples:
35
2 significant figures
48.96 4 significant figures
How many significant figures in
896.76
A. 2
B. 3
C. 4
D. 5
Rules For Significant Figures
2) Zeros between numbers (sandwiched
zeros) are all significant
Example:
304 – 3 significant digits
56.098 – 5 significant digits
How many significant figures in
1,043?
A.
B.
C.
D.
1
2
3
4
Rules For Significant Figures
3) Any zero appearing in front of a non-zero
digit is NOT significant (regardless of a
decimal)
Example:
0.876 – 3 significant digits
0.0056 – 2 significant digits
How many significant figures in
0.0008
A.
B.
C.
D.
1
3
4
5
Rules for significant figures
4) Zeros at the end of a number AND to the
right of a decimal point are significant
Examples:
72.00 – 4 significant figures
7.000000000 – 10 significant figures
How many significant figures in
5.6000
A.
B.
C.
D.
2
4
5
Help, I’m
confused!
Rules For Significant Figures
5. A) Zeros at the end of the number
WITHOUT a decimal place are NOT
significant.
Example:
3,000 – 1 significant figure
560 – 2 significant figures
How many significant figures does
453,000 have?
A.
B.
C.
D.
2
3
4
6
Rules For Significant Figures
5 B) Zeros at the end of a number to the
LEFT of a decimal point are significant
Example:
300.- Has three significant figures
4,000. – Has four significant figures
How many significant figures does
1,000. have?
A.
B.
C.
D.
1
2
3
4
How many sig figs does 305.00
have?
A.
B.
C.
D.
2
3
5
Help! I’m
confused!
How many sig figs does 0.009
have?
A.
B.
C.
D.
1
2
3
4
How many sig figs does 5,600.
A.
B.
C.
D.
1
2
3
4
Sig Figs in Calculations
A calculated answer cannot be more
precise than the measuring tool.
A calculated answer must match the
least precise measurement.
Significant figures are needed for
final answers from
1) adding or subtracting
2) multiplying or dividing
Sig Figs and Addition/Subtraction
The answer has the same number of
decimal places as the measurement
with the fewest decimal places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
Round the answer to the
correct number of significant
figures
235.05 + 19.6 + 2.1 =
A) 256.75
B) 256.8
C) 257
Round the answer to the
correct number of significant
figures
58.925 - 18.2
A) 40.725
B) 40.73
C) 40.7
Multiplying and Dividing with Sig
Figs
Round (or add zeros) to the calculated
answer until you have the same
number of significant figures as the
measurement with the fewest
significant figures.
2.19 X 4.2
A. 9
B. 9.2
C. 9.198
4.311 ÷ 0.07
A. 61.58
B. 62
C. 60