Transcript Calculating with Significant Figures

Calculating with Significant
Figures
• When we do math with these
numbers, always round to the
number of significant figures
represented by the most uncertain
number. There are rules,
depending on the operations you
perform.
Calculating with Significant
Figures: Multiplication & Division
• To determine the number of
significant figures in your answer,
look for the term with the smallest
number of significant figures,
because that is the least accurate
measurement:
Multiplication
Example:
4.56 x 1.4 = 6.384
4.56 has three significant figures and
1.4 has two significant figures,
therefore round off to two significant
figures in your answer = 6.4
Division Example:
Example: 8.315 = 0.0279027 Since 298 has
the
298
least
number of
significant figures (3),
we round the
answer to 0.0279
Multiplication & Division
Practice
a) 14 x 0.8725
b) 2,096 x 1.3
a) 67.90 ÷ 2
c) 47,249 x 0.0035
b) 5600 ÷0.368
d) 38,000 x
2.72046
e) 536 x 0.000012
c) 884.00÷76.
d) 0.0082 ÷ 1.6115
Calculating with Significant
Figures: Addition & Subtraction
• To determine the number of
significant figures in your answer,
find the term with the smallest
number of decimal places. Use
that many decimal places for your
significant figures in your answer.
Addition Example:
Example: 12.11
18.0
+ 1.013
31.123
= 31.1
Since 18.0 has just one
decimal place, we will
round off the answer to one
decimal place.
Addition & Subtraction
Practice
a) 78.50
+6.2106
(d) 62.55
143.1
+ 0.21060
b) 142.0917
– 3
,
(e)
c) 400.
– 1.43
1.0917
127.00
.716
+ 35.7
,
Rounding
Off
• Once you have determined how many significant figures
is in your answer, there are a few rules for rounding off:
1. Round down if the digit to be removed is less than 5.
1.33 rounded to two significant figures becomes 1.3
2. Round up if the digit to be removed is 5 or greater.
Rounding to two significant figures, 1.36 becomes 1.4 and 3.15
becomes 3.2.
3. If you are removing a string of numbers, only look at the
first number to the right.
Rounding 4.348 to two significant figures becomes 4.3.
4. In a series of calculations, keep the extra digits until
your final result, then round.
Scientific Notation
• The mass of a proton =
• 1.67 x 10 grams
-27
• What does this mean???
Review: What are the following
#s?
• 10
• 10
• 10
• 10
• 10
1 =10
2 =10x10=100
3 =10x10x10=1,000
4=
10,000
0=
1
•
• 10
• 10
• 10
-1
10
= .1
-2
= .01
-3
= .001
-4
= .0001
Scientific Notation uses a number
multiplied by a power of ten:
• 2000 =
• 0.004 =
3
2x10
4x10-3
Rules for Scientific Notation:
1. Add decimal point if it is missing: 3200.
2. Move decimal point so there is ONE
non-zero number to the left of it: 3.200
3. Exponent is the number of places the
decimal point was shifted: 3.200x103
4. Exponent can be positive or negative:
0.0063 = 6.3x10-3
Express in Scientific Notation
a) 4001
b) 32,560,000
c) 78,941,000,000
d) 0.00072
e) 0.00000649
f) 0.00041961