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Introduction |
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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. |
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Significant Figures and Measuring Instruments |
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The number of significant figures depends on the instrument used and accuracy required. |
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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. |
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The significant figures express number of units, rounded to the nearest such unit. |
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Approximation |
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We know that the digits of a number, one by one in order from left to right decrease in value rapidly. |
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Numbers can be rounded off to any given place. |
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When we round off a number to any given place we get an approximate value of the number. |
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Absolute Error and Percentage Relative Error |
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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. |
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Summary |
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1. We use specific number of digits to denote the value of a number to a certain degree of accuracy. |
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2. For a number between 0 and 1, the successive zeros after the decimal are not significant. |
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3. For a number with a decimal point, the final zeros are significant.
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