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| Significant Figures |
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| These express the degree of accuracy of
measurements. It is a statement which gives number of digits up to which we
are sure about their accuracy. It gives the degree of accuracy or precision
made with the instrument. In practical life we depend only on approximate
measurements. We ignore small measurements when we are computing large
measurements. For example, we may measure the length of a wall as 10 meters
and 57 centimeters or 10.57 meters. The actual length of the wall is between
10 meters 57.5 cm and 10 meters 56.5 cm. Now we can say that the length
10.57 meters is correct up to four significant figures. |
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| (a) 8.88 correct to two significant figures is 8.9, because 8.88 is nearer to 8.9 than to 8.8. |
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| (b) On the other hand 8.82 correct to two significant figures is 8.8. This is because 8.82 is nearer to 8.8 than to 8.9. |
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| Correct the number 8.5775 |
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| (a) up to 2 significant figures = 8.6 |
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| (b) up to 3 significant figures = 8.58 |
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| (c) up to 4 significant figures - 8.578 |
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| Suppose you are measuring the diameter of a cylinder using a vernier calliper as 2.38 cm. The accurate value may lie between 2.375 cm and 2.385 cm. In this case figures 2 and 3 are absolutely correct while 8 is reasonably correct. This measurement is said to be accurate up to 3 significant figures. |
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 All the digits from 1, 2, 3, 4, …., 9 are significant digits. |
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Zeros
(0s) if they occur between non-zero digits, are significant |
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| For example, in the
number- 325007, 2409, 308, zeros in between the digits are significant. |
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The
final zeros (0s) of an approximated number when expressed as decimal are
significant, e.g., |
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| (i) 8.70 meters means
approximation is to the nearest centimeters (i.e., two decimal places) |
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| (ii) 5.430 kg means
approximation is to the nearest gram (i.e., three decimal places). |
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0s
(zeros) which are used only to locate the decimal point are non-significant
e.g., 0.007, 0.09, 0.4 |
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