Transcript Significant Figures (Digits)

Significant Figures (Digits)
numbers – pure number/significant
digits are NOT applicable
 Examples of exact numbers
- 10 pennies
- 30 students
- 1 dozen
- 100 %
 Exact
Significant Figures (Digits)
Digits – a number that is part of
a measured quantity. Significant digits
only apply to measurements.
 Some examples of significant digits
- 15 cm
- 12.5 in
- 1.0 qt
 Significant
Significant Figures (Digits)
 Rules
for using significant digits
1. Apply only to measured quantities
2. Must include units
3. Must reflect the precision of the
measuring device.
Significant Figures (Digits)
 Significant
digits apply only to
MEASURED quantities
a. length
b. volume
c. mass/weight
Significant Figures (Digits)
 All
non-zero digits are significant
a. 531 contains 3 significant digits
b. 7318 contains 4 significant digits
c. 4 contains 1 significant digit
Significant Figures (Digits)
 Zeros
BETWEEN non-zero digits are
significant
a. 101 contains 3 significant digits
b. 98705 contains 5 significant digits
Significant Figures (Digits)
 Trailing
zeros are NOT significant
a. 10 contains 1 significant digit
b. 1010 contains 3 significant digits
c. 10000 contains 1 significant digit
Significant Figures (Digits)
 Trailing
zeros are NOT significant
a. 10 contains 1 significant digit
b. 1010 contains 3 significant digits
c. 10000 contains 1 significant digit
 UNLESS there is a decimal point!
a. 10. contains 2 significant digits
b. 1010. contains 4 significant digits
c. 10000. contains 5 significant digits
Significant Figures (Digits)
 Zeros
AFTER a decimal point are
significant
a. 10.0 contains 3 significant digits
b. 1010.00 contains 6 significant digits
Significant Figures (Digits)
 Zeros
AFTER a decimal point are
significant
a. 10.0 contains 3 significant digits
b. 1010.00 contains 6 significant digits
 UNLESS the function of the zero is to
locate the decimal point
a. 0.01 contains 1 significant digits
b. 0.0011 contains 2 significant digits
Significant Figures (Digits)
 Zeros
AFTER a decimal point and AFTER
a significant digit are significant
a. 0.010 contains 2 significant digits
b. 0.0100 contains 3 significant digits
c. 0.010010 contains 5 significant digits
Significant Figures (Digits)
 Non-zero
digits BEFORE a decimal point
makes all zeros significant
a. 1.00 contains 3 significant digits
b. 1.010 contains 4 significant digits
c. 1.011010 contains 7 significant digits
Significant Figures (Digits)
 Significant
digits do not apply to counting
numbers or exact numbers
a. 47 people - counting number
b. 63 cars entered the race – counting number
c. 10 pennies = 1 dime exact number
d. 12 apples = 1 dozen
Significant Figures (Digits)
 Adding
with significant digits:
37.25 cm
+ 4. 387 cm
41.637 cm
The answer to this addition can contain only
2 digits beyond the decimal point. The
answer to this problem is 41.64 cm, a result
based on rounding.
Significant Figures (Digits)
 Rounding
- rounding is the last step in
completing a problem and expressing the
answer with the correct number of
significant digits. Note: Never round until
the last step/the final answer.
Significant Figures (Digits)
 Rules
for Rounding
 If the rounding digit is greater than 5,
increase the preceding digit by 1
 If the rounding digit is less than 5, leave the
preceding digit alone
 If the rounding digit is 5, then make the
preceding digit EVEN!
Significant Figures (Digits)
 Multiplying
with significant digits:
37.25 cm
x 4. 387 cm
2
163.41575 cm
The answer to this multiplication can
contain only 4 significant digits. Therefore,
the answer to this problem is 163.4 cm.
Significant Figures (Digits)
 Round
47.8485 cm to 2 significant digits
Significant Figures (Digits)
 Round
47.8485 cm to 2 significant digits
 The answer is 48 cm or better 48.cm
 Now, round 47.8485 cm to 3 significant
digits
Significant Figures (Digits)
 Round
47.8485 cm to 2 significant digits
 The answer is 48 cm or better 48. cm
 Now, round 47.8485 cm to 3 significant
digits
 The answer is 47.8 cm
 Now, round 47.8485 to 4 significant digits
Significant Figures (Digits)
 Round
47.8485 cm to 2 significant digits
 The answer is 48 cm or better 48. cm
 Now, round 47.8485 cm to 3 significant digits
 The answer is 47.8 cm
 Now, round 47.8485 cm to 4 significant digits
 The answer is 47.85 cm
 Finally, round 47.8485 to 5 significant digits
Significant Figures (Digits)
 Round
47.8485 cm to 2 significant digits
 The answer is 48 cm or better 48. cm
 Now, round 47.8485 cm to 3 significant digits
 The answer is 47.8 cm
 Now, round 47.8485 to 4 significant digits
 The answer is 47.85 cm
 Finally,
round 47.8485 cm to 5 significant
digits
 The answer is 47.848 cm
Significant Figures (Digits)
 Round
0.092558 to one significant digit
Significant Figures (Digits)
 Round
0.092558 g to one significant digit
 The answer is 0.09 g
 Now, round 0.092558 g to three significant digits
Significant Figures (Digits)
 Round
0.092558 g to one significant digit
 The answer is 0.09 g
 Now, round 0.092558 g to three significant digits
 The answer is 0.0926 g
 Now, round 0.092558 g to four significant digits
Significant Figures (Digits)
 Round
0.092558 g to one significant digit
 The answer is 0.09 g
 Now, round 0.092558 g to three significant digits
 The answer is 0.0926 g
 Now, round 0.092558g to four significant digits
 The answer is 0.09256 g
Exponential Notation
 Sometimes
we deal with very large or very small
numbers. It is difficult to write these numbers
with all of the necessary zeros just to show where
the decimal point should be. Instead we have
developed a technique which allows us to write
these numbers in a form which easily shows the
number of significant digits and the location of the
decimal point. The technique is call exponential
notation or scientific notation.
Scientific Notation
 Scientific
Notation (Exponential Notation) writes
all numbers using this format:
p
D.DD x 10
 D represents the significant digits. Note that only
one digit remains to the LEFT of the decimal
point. The remaining significant digits appear to
the right of the decimal point.
 P, the power of the base 10, represents the number
of spaces that the decimal point had to be moved.
Scientific Notation
 Write
9600 in scientific notation.
 First, determine the number of significant digits in
the number. In this case there are two (2).
 Since there is no decimal point in this number,
place a decimal point at the end of the number:
9600.
 Now, move the decimal point to the LEFT until
there is only a single digit to the left of the
decimal point.
Scientific Notation
 Now,
move the decimal point to the LEFT until
there is only a single digit to the left of the
decimal point.
 The result is: 9.600; since the result should have 2
significant digits, we write the first part as:
p
9.6 x 10
 What is the value for p? There are two items that
must be considered to determine the value of p.
What are they?
Scientific Notation
 What
is the value for p? There are two items that
must be considered to determine the value of p.
What are they?
 (1) How many spaces was the decimal point
moved? In our example the answer is 3.
 (2) In which direction, Right (-) or Left (+), was
the decimal point moved? In our case it was
moved to the LEFT. The sign will be +.
Scientific Notation
 The
final notation for our example will be:
3
9.6 x 10
 Write 0.00602 in scientific notation.
Scientific Notation
 Write
0.00602 in scientific notation.
 There are 3 significant digits in this
number.
 Move the decimal point three spaces.
-3
 The result is: 6.02 x 10
Unit Factors
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Conversion Factors
Used to convert from one unit to
another unit in the same measuring
system or a different measuring system
Use the “from” and “to” method to
determine the values to be placed in the
conversion factor
Unit Factors
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100 cm  1 meter
This is an EXACT number - there are
exactly 100 cm in 1 meter by definition;
the rules for significant digits do not
apply
Practice using conversion/unit factors
Unit Factors

1m( to) 
 27cm
  0.27m
100cm( from) 
