Linear Algebra:
Significant Figures:
When we speak about the word significant,the first thing that comes to our mind is Fitted or designed to signify or make known, or that which has significance; a sign; a token; a symbol.The basic introduction is we use specific number of digits to denote an exact value of a number for required accuracy.The digits used for such a purpose are called significant figures.Next in line is how do we measure these significant figure,to understand the measurement of these figures is of utmost importance. The common question we face is what does significant number depend on???The number of significant figures depends on the instrument used and accuracy required.It is wrong to record diameter as 2 cm. It means the reading is approximated to the nearest 1 cm. If the exact reading is 2 cm then it should be recorded as 2.0 cm.The significant figures express number of units, rounded to the nearest such unit.
Let us now understand the importance of the expression of digits.The outcome of any situation or thing solely depends on how well it is expressed.If something is expressed to the best of its ability the better will be the outcome.The reliability of a measurement is indicated by the number of digits used to represent it. To express it more accurately we express it with digits that are known with certainty. These are called as Significant figures. They contain all the certain digits plus one doubtful digit in a number.
If the volume of the liquid is reported to be 23।5mL, it means that digits 2 and 3 are certain while 5 is uncertain. Therefore, the number 23.5 has three significant figures. The number of significant figures conveys that except the last digits all others are correct. The number of digits depends on the precision of the scale used.
Approximation:
We know that the digits of a number, one by one in order from left to right decrease in value rapidly.Numbers can be rounded off to any given place.When we round off a number to any given place we get an approximate value of the number.Absolute Error and Percentage Relative Error.The difference between these two values is called the absolute error.
Absolute Error = Original number - Approximated number
The ratio of the absolute error and the original number expressed in percentage form is called percentage relative error.
Summary:
1. We use specific number of digits to denote the value of a number to a certain degree of accuracy.
2. For a number between 0 and 1, the successive zeros after the decimal are not significant.
3. For a number with a decimal point, the final zeros are significant.
Hope you like the above example of Significant Figures.Please leave your comments, if you have any doubts.
Significant Figures:
When we speak about the word significant,the first thing that comes to our mind is Fitted or designed to signify or make known, or that which has significance; a sign; a token; a symbol.The basic introduction is we use specific number of digits to denote an exact value of a number for required accuracy.The digits used for such a purpose are called significant figures.Next in line is how do we measure these significant figure,to understand the measurement of these figures is of utmost importance. The common question we face is what does significant number depend on???The number of significant figures depends on the instrument used and accuracy required.It is wrong to record diameter as 2 cm. It means the reading is approximated to the nearest 1 cm. If the exact reading is 2 cm then it should be recorded as 2.0 cm.The significant figures express number of units, rounded to the nearest such unit.
Let us now understand the importance of the expression of digits.The outcome of any situation or thing solely depends on how well it is expressed.If something is expressed to the best of its ability the better will be the outcome.The reliability of a measurement is indicated by the number of digits used to represent it. To express it more accurately we express it with digits that are known with certainty. These are called as Significant figures. They contain all the certain digits plus one doubtful digit in a number.
If the volume of the liquid is reported to be 23।5mL, it means that digits 2 and 3 are certain while 5 is uncertain. Therefore, the number 23.5 has three significant figures. The number of significant figures conveys that except the last digits all others are correct. The number of digits depends on the precision of the scale used.
Approximation:
We know that the digits of a number, one by one in order from left to right decrease in value rapidly.Numbers can be rounded off to any given place.When we round off a number to any given place we get an approximate value of the number.Absolute Error and Percentage Relative Error.The difference between these two values is called the absolute error.
Absolute Error = Original number - Approximated number
The ratio of the absolute error and the original number expressed in percentage form is called percentage relative error.
Summary:
1. We use specific number of digits to denote the value of a number to a certain degree of accuracy.
2. For a number between 0 and 1, the successive zeros after the decimal are not significant.
3. For a number with a decimal point, the final zeros are significant.
Hope you like the above example of Significant Figures.Please leave your comments, if you have any doubts.
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