SIGNIFICANT
FIGURES:
“All the accurately
known digits in a value and the first doubtful digit are known as significant
figures.” In
the measurement of any physical quantity the number of digits about which we
are sure are called significant figures All physical measurements involve some
degree of inaccuracy due to human error, instrumental error or due to both and
therefore the knowledge of precision of a measurement is very important. A
significant figure is that which is known to be reasonably reliable. The last
figure being reasonably correct guarantees the certainty of the preceding
figures.
RULES
FOR COUNTING SIGNIFICANT FIGURES:
(i) In whole number values, all the digits except zeros
at the right side are recognized as significant figures.
(ii) In decimal number values the zeros at the right side
of the number are counted as significant figures but the zeros at the left side
are not taken as significant figures.
(iii) Power or exponents to a certain base are not taken
as significant figures.
(iv) In addition and subtraction process, the result
should be rounded off to contain as many as decimal places as contained in the
value of least number of decimal place.
(v) In multiplication and division process, the result
should be rounded off to contain as many as significant figures as contained in
the factor of least significant figures.
FOR
EXAMPLE:
S.NO
|
Value
|
No. of significant
figures
|
1
|
0.00045
|
2(4,5)
|
2
|
1.2000
|
5(1,2,0,0,0)
|
3
|
505
|
3(5,0,5)
|
4
|
34000
|
2(3,4)
|
5
|
6.67 x 1032
|
3(6,6,7)
|
The following rule can
be used to convert numbers into scientific notation: The exponent in
scientific notation is equal to the number of times the decimal point must be
moved to produce a number between 1 and 10. In 1990 the population of
Chicago was 6,070,000 . To convert this number to scientific notation we move
the decimal point to the left six times.
6,070,000 = 6.070 x 106
|
To translate
10,300,000,000,000,000,000,000 carbon atoms into scientific notation, we move
the decimal point to the left 22 times.
10,300,000,000,000,000,000,000 = 1.03 x 1022
To convert numbers
smaller than 1 into scientific notation, we have to move the decimal point to
the right. The decimal point in 0.000985, for example, must be moved to the
right four times.
0.000985 = 9.85 x 10-4
Converting
0.000,000,000,000,000,000,000,020 grams per carbon atom into scientific
notation involves moving the decimal point to the right 23 times.
0.000,000,000,000,000,000,000,020 = 2.0 x 10-23
The primary reason for
converting numbers into scientific notation is to make calculations with
unusually large or small numbers less cumbersome. Because zeros are no longer
used to set the decimal point, all of the digits in a number in scientific
notation are significant, as shown by the following examples.
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