Transcript Measuring with Precision

Working with
Significant
Figures
Exact
Numbers
•Some numbers are exact, either because:
•We count them (there are 14 elephants)
•By definition (1 inch = 2.54 cm)
•These numbers have no limit of significant
digits
•For the rest of our measurements and
calculations, we need to keep track of Sig
Figs!
Significant Figures
RULE #1
• Include ONE estimated digit
5.2 cm
Sig Fig Rule #2
• Count all non-zero integers:
• 452 (3 sig figs)
• 59,294 (5 sig figs)
• 28 (2 sig figs)
• 893,438,894 (9 sig figs)
Sig Fig Rule #3
• Any zeros coming before all the nonzero digits don’t count:
• 0.67291
• 0.00239
• 0.00004
(5 sig figs)
(3 sig figs)
(1 sig fig)
Sig Fig Rule #4
• DO count any zeros trapped between
non-zero digits:
• 5.0031 (5 sig figs)
• 80,045 (5 sig figs)
• 0.3906 (4 sig figs)
• 0.004900302 (7 sig figs)
Sig Fig Rule # 5
• Count zeros to the right of all non-zero
digits only if there is a decimal:
• 6.300 (4 sig figs)
• 470.00 (5 sig figs)
• 200 (1 sig fig)
• 200. (3 sig figs)
The Chart
• Tape this into your Lab Journal for your
reference and practice.
Some Practice
• Give the number of significant figures for each
example
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
8.9007
5,000
0.0396
10,700.
0.2000
7.003051
0.00175
4,602,390
0.000300
60
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
• Sig figs in answer = Sig figs in the
term with the smallest number of
Sig figs, 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
298
➡Since 298 has the least
number of significant
figures (3), we round the
answer to 0.0279
Multiplication & Division
Practice
a) 14 x 0.8725
f) 67.90 ÷ 2
b) 2,096 x 1.3
g) 5600 ÷0.368
c) 47,249 x 0.0035
h) 884.00÷76.
d) 38,000 x 2.72046
i) 0.0082 ÷ 1.6115
e) 536 x 0.000012
Calculating with Significant Figures:
Addition & Subtraction
• Sig Figs in answer = the term with
the fewest decimal places. Use
that many decimal places 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.
Homework
• Significant Figures Practice