Transcript Significant Figures and Rounding

Significant Figures and Rounding
Significant Figures
 Significant figures - show accuracy in measurements &
calculations
 Significant figures in a measurement consist of all of the
digits known with certainty plus one digit that is an estimate.
 The number of significant figures in a measurement indicates
to precision in the measurement it is.
A balance that reads to the 1.0 gram is less certain in a
measurement that a balance that reads to 1.000 grams.
Rules for Identifying sig. figs. In a
Measurement
 The digits 1 through 9 ( all non-zero digits) are ALWAYS
significant.
243
Has 3 significant figures
1.287
Four significant figures
 How many significant figures are in 142.32
 5 Significant digits
 How many significant figures are in 3.1
 2 significant digits
Rules for Identifying sig. figs. In a
Measurement
 Middle zeros are ALWAYS significant figures (zeros
between non-zero digits)
207
Three significant figures
1.0032
Five significant figures
 How many significant figures are in 207.5
 4 significant digits
 How many significant figures are in 60,007
 5 significant digits
Rules for Identifying sig. figs. In a
Measurement
 Leading zeros are NEVER significant. Leading zeros are
zeros that occur at the beginning of a number. Leading
zeros function to indicate the position of the decimal
point.
0.0045
Two significant figures
0.034009
Five significant figures
 How many significant figures are in 0.0307
 3 significant digits
 How many significant figures are in 0.0037009
 5 significant digits
Rules for Identifying sig. figs. In a
Measurement
 Ending zeros are zeros at the end of the number. They are
SOMETIMES significant. They ARE significant if there is a
decimal point anywhere in the number. If no decimal
point, ending zeros are NOT significant.
200.0
Four significant figures
2000.
Four significant figures
200
One significant figure
 How many significant figures are in 62.00
 4 significant digits
 How many significant figures are in 24.70
 4 significant digits
 How many significant figures are in 360,000
 2 significant digits
 Counting, exact and defined numbers have an infinite
number of significant figures.
 Pi 3.1415926535893238………
 Avogadro’s number 6.0221415 x 10^23
 A bakers dozen
 The do not affect the number of sig figs in your final answer
EXERCISE 1
A. 10423
B. 1230.0
C. 150
D. 0.0032
E. 3300
F. 10.0
G. 0.05010
10423 5 sig figs
1230.0 5 sig figs
150
2 sig figs
0.0032
3300
10.0
2 sig figs
2 sig figs
3 sig figs
0.05010
4 sig figs
Rounding
Rounding is the process of deleting extra digits from a
calculated number.
1. If the first digit to be dropped is less than 5, that
digit and all the digits that follow it are simply
dropped.
1.673 rounded to three significant figures
becomes 1.67
2.If the first digit to be dropped is greater than or
equal to 5, the excess digits are all dropped and the last
significant figure is rounded up.
62.873 rounded to three significant figures
becomes 62.9
Round The following
A. 423.78 to three significant figures
B. 0.000123 to two significant figures
C. 22.550 to four significant figures
D. 129.6 to three significant figures
E. 0.365 to one significant figure
F. 7.206 to three significant figures
424
0.00012
22.55
130. (must have decimal)
0.4
7.21
Calculations Using Significant Figures
 A calculated number cannot be more precise than the
data numbers used to calculate it. In other words: the
answer can’t be more precise than any of the original
numbers in the problem.
Addition and Subtraction
*Two different rules apply: The Rule for Addition & Subtraction is DIFFERENT
than the Rule for Multiplication and Division
1. Addition & Subtraction
In addition and subtraction, the last digit in the answer must be expressed to
the same decimal place value as the entry with the ____least________
accurate decimal position.
5.72
0.00648
37.916__
43.7008
l
78.4
-3.628
74.772
(accurate to the hundredths position)
(accurate to the hundred thousandths position)
(accurate to the thousandths position)
Becomes 43.70 to the hundredths position
(accurate to the tenths position)
(accurate to the thousandths position)
Becomes 74.8 to the tenths position
Addition and Subtraction
*Write the given calculated answer in the correct number of significant
figures. Look at decimal places only
a. 3.64 + 0.0829 = 3.7229
b. 67.4 + 4.28 = 71.68
c. 3.289 – 0.66 = 2.629
d. 5.976 – 0.497 = 5.497
e. 269 + 3.27 + 4.6 = 276.87
f. 7.2 + 0.69 – 0.0324 = 7.8666
3.72
71.7
2.63
no change
no decimal place in first number
7.9
277
Multiplication and Division
 In multiplication and division the number of significant
figures in the product or quotient must be the same as in
the number in the calculation that contains the least
significant figures
This is the rule we mainly use!!!
 6.038 x 2.57 = 15.51766
 Correct answer is 15.5 because the three significant digits in
2.57 limits our answers to three significant digits
 120.0 ÷ 4.000 = 30
 Correct answer is 30.00 because each entry has four
significant digits so your answer must have four significant
digits.
 (3.130 x 3.14) ÷ 3.1 = 3.170387097
 Correct answer is 3.2 because the least number of significant
digits in the entries is two so our answer must only have two
significant digits.
Multiplication and Division Practice
.
Count total number of Sig Figs!!!!
a. 3.751 x 0.42 = 1.57542
1.6
b. 6.7321 x 0.0021 = 0.01420041
0.014
c. 3.27 / 4.6 = 0.710869565
0.71
d. 49.7 / 0.05976 = 831.6599732
832
e. (7.2 x 0.69) / 3.24 = 0.866666666
0.87
f.
269 / (3.270 x 4.6) = 17.88323602
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