Various statistical term definitions
Significant figures: may be define a maximum digit number required to analyze a given value scientifically with a precision measurement.
This way is very significant in messaging the exact meaning and status of each digit. The fact is that a lot of population did not have required Knowledge for making used of significant figures, as such living experimentally to appear confused
Often sometimes we may think that 0 is not a significant figure, but the fact of this is where the zero is found, Zero (0) can be a significant figure base on the location of it measured value.
In a general perspective, zero are significant if they found;
To occurs in the center of a number
Or if they occur at the right hand side end of the decimal point.
In the measurement, the significant figure number is independent of the decimal point placement.
What it means is that number of significant figures in a measurement did not depend on the place where decimal point is found.
Example of zero that are significant figure are underline; 602, 0.0602, 9090, 0.5030. But there may be a confusion when figure like 82400 is written in respect of the significant figures. But never the less, it can be written in the following ways.
8.24 x 104 – 3 significant figures
8.240 x 104 – 4 significant figures
8.2400 x 104 – 5 significant figures
Remember that the first figures that is ambiguous is the last significant figures.
How to Round off Number
Often one of the major problems faced by scientist base on the significant figures, is when there are arithmetical operation that was performed and there is need of rounding off the answers. Such operation it could be addition/subtraction, multiplication/division.
Rounding of number must be done on the final answer not on the intermediate result, on doing that, the accumulation of round off error will be drastically reduce.
Addition and Subtraction
Note that general guideline of rounding of number is that all number involved should be express in the same exponent and should be align with respect to the decimal point.
Rounding off the answer according to the number of decimal point in the number with less or fewest decimal places.
Example (a) 13.344137
+ 16.347799
+ 43.313
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Ans = 72.504936
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The two last digit of the answer is not significant, our
Final answer is 72.505
If you are adding or you are subtracting numbers express in a scientific notation, it should first of all be converted to the same exponent.
Example (b) 2.353 x 105
+ 4.314 x 103
+ 1.798 x 106
Convert to the same exponent
2.353 x 105 2.353 x 105
+ 4.314 x 103 → + 0.04314 x 105
+ 1.798 x 106 + 0.0798 x 105
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+ 2.47594 x 105
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Now we round of the answer to the lowest decimal point.
Final answer is 2.48 x 105.
Multiplication and Division
The operation should be limited to the digit number contained in the number with lowest significant figures.
Example (a) 2.26 x 10 -5
x 2.78
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6.90 x 10-5
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Example (b) 5.3179 x 1012
x 4.6 x 10-19
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2.45 x 10-6
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Example (c) 35.60
x 3.46287
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123.278172
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Be informed that power of 10 did not have an influence on the number of figures that must be retained.
One again we will be summarizing the rounding of rule for you on this our final note;
- If the digit following the last numbers is higher than 5, then the number is rounded up to the next higher number.
- If the number is bellow or less than 5, the number should be rounded off to the present figure of the last significant figures.
For example
8.47 should be rounded off to 8.5
8.44 should be rounded off to 8.4
- if the last digit is 5, then the following round off should be adopted
5.65 should rounded off to 5.6 not 5.7
5.78 should rounded off to 5.8
5.55 should rounded off to 4.6
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