Transcript Accuracy, Precision, Signficant Digits and Scientific Notation

Accuracy, Precision,
Signficant Digits and
Scientific Notation
Accuracy and Precision
• Accuracy – refers to how close a
given quantity is to an accepted or
expected value (page 19)
• Precision – refers to how exact a
measurement is. It also refers to how
close measurements are to each
other (see page 16 and 19)
Example
Watch the following video
clip
video
Rules for Significant Digits
1. Digits from 1-9 are always significant.
2. Zeros between two other significant
digits are always significant
3. One or more additional zeros to the
right of both the decimal place and
another significant digit are significant.
4. Zeros used solely for spacing the
decimal point (placeholders) are not
significant.
Examples of Significant Digits
EXAMPLES
# OF SIG. DIG.
COMMENT
453 kg
3
All non-zero digits are
always significant.
5057 L
4
Zeros between 2 sig.
dig. are significant.
5.00
3
Additional zeros to the
right of decimal and a sig.
dig. are significant.
0.007
1
Placeholders are not
sig.
Multiplying and Dividing
• RULE: When multiplying or dividing,
your answer may only show as many
significant digits as the multiplied
or divided measurement showing the
least number of significant digits
Example:
When multiplying 22.37 cm x 3.10 cm x 85.75 cm =
5946.50525 cm3
We look to the original problem and check the number of
significant digits in each of the original measurements:
22.37 shows 4 significant digits.
3.10 shows 3 significant digits.
85.75 shows 4 significant digits.
Our answer can only show 3 significant digits because that
is the least number of significant digits in the original
problem. 5946.50525 shows 9 significant digits, we must
round to the tens place in order to show only 3 significant
digits.
Our final answer becomes 5.95 x 103 cm3.
Scientific Notation
•
Use this method to express large numbers
and doing calculations by using powers of
10
• To do this, count the number of places
you have to move the decimal point to
yield a value between 1 and 10. This
counted number is the exponent. The
exponent is positive if the original number
is greater than 10 and negative if the
original number is less than 10
Examples:
a. 150 000 000 000 is 1.5 x 1011m
b. 0.000 000 000 050 is 5.0 x 10-11m
Adding and Subtracting
• RULE: When adding or subtracting
your answer can only show as many
decimal places as the measurement
having the fewest number of
decimal places.
Example: When we add 3.76 g + 14.83 g +
2.1 g = 20.69 g
We look to the original problem to see
the number of decimal places shown in
each of the original measurements.
2.1 shows the least number of decimal
places. We must round our answer, 20.69,
to one decimal place (the tenth place).
Our final answer is 20.7 g
Practice – sig figs
1) 400
2)
200.0
3)
0.0001
4)
5) 3.2 x 102
6)
0.00530
7)
22 568
8) 4755.50
Answers: 1) 1
2) 4
3) 1
4) 3
5) 2
6) 3
7) 5
8) 6
218
Practice – Adding and substracting
1)
4.60 + 3 =
4) 200 - 87.3 =
Answers 1) 8
2) 0.06
3) 79.423
2)
0.008 + 0.05 =
3)
=
5)
67.5 - 0.009 =
6) 71.86 - 13.1 =
4) 113
5)
67.5
6)
58.8
22.4420 + 56.981
Practice – Multiplying and
dividing
1)
50.0 x 2.00 =
4) 51 / 7 =
Answers 1) 1.00 x 102
2) 59
2)2.3 x 3.45 x 7.42 =
3) 1.0007 x 0.009 =
5)
6) 0.003 / 5 =
3) 0.009
208 / 9.0 =
4) 7
5)
23
6)
0.0006
Rounding Rules
1. If your answer ends in a number
greater than 5, increase the
preceding digit by 1.
Example: 2.346 can be rounded to 2.35
2. If your answer end with a number
that is less than 5, leave the
preceding number unchanged
Example: 5.73 can be rounded as 5.7
Rounding rules continued
3. If you answer ends with 5, increase
the preceding number by 1 if it is
odd. Leave the preceding number
unchanged if it is even.
For example, 18.35 can be round to
18.4, but 18.25 is rounded to 18.2