Scientific Notation
In which any
number can be represented in the form N × 10n(Where n is an
exponent having positive or negative values and N can vary between 1 to
10). e.g. We can write 232.508 as 2.32508 x102in scientific
notation. Similarly, 0.00016 can be written as 1.6 x 10–4.
Precision refers to the closeness of various measurements for the same quantity. Accuracy is the agreement of a particular value to the true value of the result
Significant Figures
The reliability of
a measurement is indicated by the number of digits used to represent it.
To express it more accuratelywe express it with digits that are known
with certainty. These are called as Significant figures. They contain all
thecertain digits plus one doubtful digit in a number.
Rules for Determining the Number of Significant Figures
All non-zero
digits are significant. For example, 6.9 has two significant figures,
while 2.16 has three significantfigures. The decimal place does not
determine the number of significant figures.
A zero becomes
significant in case it comes in between non zero numbers. For example,
2.003 has four significantfigures, 4.02 has three significant figures. Zeros at
the beginning of a number are not significant. For example, 0.002 has one
significant figure while 0.0045has two significant figures.
All zeros placed
to the right of a number are significant. For example, 16.0 has three
significant figures, while 16.00has four significant figures. Zeros at
the end of a number without decimal point are ambiguous.
In exponential
notations, the numerical portion represents the number of significant
figures. For example, 0.00045 isexpressed as 4.5 x 10-4in terms of
scientific notations. The number of significant figures in this number is
2, while inAvogadro's number (6.023 x 1023) it is
four.
The decimal point
does not count towards the number of significant figures. For example,
the number 345601 has sixsignificant figures but can be written in
different ways, as 345.601 or 0.345601 or 3.45601 all having same number
ofsignificant figures.
Retention of Significant Figures - Rounding off Figures
The rounding off
procedure is applied to retain the required number of significant
figures.
1. If the digit
coming after the desired number of significant figures happens to be more
than 5, the precedingsignificant figure is increased by one, 4.317 is
rounded off to 4.32.
2. If the digit
involved is less than 5, it is neglected and the preceding significant
figure remains unchanged, 4.312 isrounded off to 4.31.
3. If the digit
happens to be 5, the last mentioned or preceding significant figure is
increased by one only in case ithappens to be odd. In case of even figure,
the preceding digit remains unchanged. 8.375 is rounded off to 8.38
while8.365 is rounded off to 8.36.
Dimensional Analysis
During calculations generally there is a need to
convert units from one system to other. This is called factor label
method or unit factor method or dimensional analysis.
For example- 5
feet and 2 inches (height of an Indian female) is to converted in SI
unit
1 inch = 2.54 x 10-2m
then, 5 feet and 2 inch = 62
inch
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