Download About Significant Figures Examples

About Significant
Figures: Examples
TABLE OF CONTENTS
Determining the Number of Significant Figures ................................................................ 1
Rule #1 – All non-zero integers are always considered significant................................ 1
Rule #2 – All zeros bounded by non-zero integers are always considered significant... 1
Rule #3 – Leading zeros are non-significant .................................................................. 1
Rule #4a – Trailing zeros are non-significant in numbers without a decimal point ....... 1
Rule #4b - Trailing zeros are significant in numbers with a decimal point .................... 1
Rule #5 – Exact numbers and defined numbers have an infinite number of significant
figures
2
Significant Figures in Calculations..................................................................................... 2
Addition and Subtraction ................................................................................................ 2
Multiplication and Division ............................................................................................ 2
Combining Operations .................................................................................................... 3
Logarithms and Anti-Logarithms ................................................................................... 4
About Significant Figures: Examples
Determining the Number of Significant Figures
Rule #1 – All non-zero integers are always considered significant
►
4,326 and 43.26
4 significant figures
Rule #2 – All zeros bounded by non-zero integers are always
considered significant
►
11, 001
5 significant figures
10037.01
7 significant figures
Rule #3 – Leading zeros are non-significant
►
0.0000072
2 significant figures
0.0030025
5 significant figures
Rule #4a – Trailing zeros are non-significant in numbers without
a decimal point
►
2, 036, 000
4 significant figures
1, 200
2 significant figures
Rule #4b - Trailing zeros are significant in numbers with a
decimal point
►
0.00011100
5 significant figures
1.72500
6 significant figures
2700.
3 significant figures
1
Rule #5 – Exact numbers and defined numbers have an infinite
number of significant figures
►
Counting 22 cows is an example of an ‘exact number’
1 m = 3.28 ft 3.28 ft is considered as a ‘defined number’
Significant Figures in Calculations
Addition and Subtraction
►
27.534 + 999.99
= 1027.524 (unrounded)
= 1027.52 (rounded)
The operand with the fewest number of decimal places is
999.99 with only two decimal places. Thus, the answer must be
rounded to only 2 decimal places.
Multiplication and Division
►
Solve for x, and express the answer with appropriate number of
significant figures:
(11.027)(x) = (125135.1)(2362.15)
x = (125135.1)(2362.15)
11.027
Step #1 – identify the operand with the lowest number of significant
figures.
11.027
– 5 significant figures  fewest sig. fig.’s
125135.1
2362.15
– 7 significant figures
– 6 significant figures
2
Step #2 – express the final answer with the same number of
significant figures as that of the operand identified in step #1
x = (125135.1)(2362.15)
11.027
x = 26805829.007436292736011607871588
= 2.6805 x 107
The final answer is rounded to only 5 significant figures.
Combining Operations
►
Suppose you want to evaluate the following expression:
25.821 – 1.7 x (231.32 – 157.9829)
Recall “BEDMAS” to solve this question and make note of the
remaining number of significant figures after each step of the
calculation.
1)
Evaluate the expression inside the parentheses (brackets):
231.32 – 157.9829 = 73.33
2)
Perform the multiplication:
1.7 x 73.33 = 120
3)
Perform the subtraction
25.821 – 120 = -94
Final answer: -94
3
Explanation:
In step 1, the operand with the least number of decimal places is
231.32 – it has 2 decimal places. Thus, the answer can only have 2
decimal places.
In step 2, the operand with the least number of significant figures is
1.7 – it has 2 significant figures. Thus, the answer is rounded to 2
significant figures.
In step 3, the operand with the least number of decimal place is 120 –
it has no decimal places. Thus, the final answer only has no decimal
places.
Logarithms and Anti-Logarithms
►
Log10 17.2 = 1.23553
logarithmic answer
The number 1 illustrates the characteristic of the logarithm
The numbers 23553 illustrate the mantissa of the logarithm
►
Log10 11.354 = 1.0551489
1.05515)
(answer should be rounded to
11.354 has 4 significant figures, and therefore the mantissa of
the logarithmic answer should also have 4 significant figures.
Thus, the logarithmic answer should be rounded to 1.05515.
►
Log10 10045 = 4.0019499
(answer should be rounded to 4.00194)
10045 has 5 significant figures, and therefore the mantissa of
the logarithmic answer should also have 5 significant figures.
Thus, the logarithmic answer should be rounded to 4.00194
(recall that the exponential value of the logarithm, 4, is not
significant because it represents the magnitude of the original
number and thus 4 is not counted as a significant figure).
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