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SIGNIFICANT FIGURES are digits, expressed in integer or decimal form, that begins with the leftmost nonzero digit and extend to the right to the precision limit of the calculations or measuring devices used to obtain the number.
Retention of digits: Retain enough significant figures in data so that only the value of the rightmost digit is uncertain.
Example:
If a pipet is graduated accurately in tenths of a milliliter, then the uncertainty of measurement would be expressed in hundredths of an ml. This is because 0.01ml represents the limits of interpolation. By reporting the value of a measurement using this pipet to the hundredths of an ml, it is implied that the actual value of the measurement is within +/-0.05ml of the reported value.
THEREFORE, for a number to have all significant figures, all digits except the rightmost must be correct, and the error in the rightmost digit must be less than or equal to one-half the value of the units of the rightmost digit.
1) All nonzero digits are significant.
2) All zeros between nonzero digits are significant.
3) All zeros to the right of a decimal point are significant for numbers greater than or equal to one.
4) For numbers less than one, zeros to the right of a decimal point, but to the left of a nonzero number are NOT significant. The zeros in this situation simply establish the units of the nonzero digits (tenths, hundredths, etc.).
5) Zeros to the left of a nonzero digit but to the left of an implied decimal may or may not be significant, depending on the precision of the determination. The zeros may simply serve to establish the units of the nonzero digits. If the zero is significant, a line should be drawn over the significant zero to indicate such.
Addition and Subtraction:
When adding and subtracting figures with differing numbers of digits adjust the number of significant digits appearing to the right of the decimal point so that all figures have the same number of significant digits appearing to the right of the decimal point.
EXAMPLE:
0.0213 = 0.02
29.64 = 29.64
1.056931 = 1.06
SUM = 30.72
Multiplication and Division:
When multiplying and dividing figures with differing numbers of significant digits, reduce the number of significant digits to the same number as present in the figure with the fewest significant digits.
EXAMPLE:
0.0211 X 25.63 X 1.05881 =>0.0211 has fewest significant figures
Reduces to-
0.0211 X 25.6 X 1.06 = 0.5725696 = 0.573