Definition: Significant figures are all zero and nonzero digits which are recorded from a measuring device and the first approximated digit. All digits obtained from a digital instrument are significant. For example, when measuring a temperature that falls directly between 21 and 22 degrees, a reading of 21.5 would be a value recorded to the correct significant figures. The amount of uncertainty in an approximated digit will vary depending on the measuring device used. However, when using the digital balance, record all numbers which appear even if they are zeros.

Postulates for Recognizing Significant Figures:

A. All nonzero numbers are significant. 2765 = 4 sig. Figs.

B. Zeros before a decimal are not significant. They are placed there as a formality to enhance the view of the decimal point. 0.55 = 2 sig. Figs.

C. Zeros between significant digits are significant. 403 = 3 sig. Figs.

D. Zeros used to indicate precision (to the right of decimal and significant digits) are significant. 14.00 = 4 s.f. 0.880 = 3 s.f.

E. Placeholder zeros are not significant. 0.005 = 1 s.f. 1500 = 2 s.f.     1.50 X 103 = 3 s.f.

F. All digits in the nonexponential (front) portion of a scientific notation number are significant. 2.6 X 10-4 = 2 s.f.

G. Numbers which are "exact" (such as many conversion factors) have an infinite number of significant figures. For example, 100 cm per 1m is an exact relationship. Both 100 cm and 1m have an infinite(¥ ) number of significant figures.

H. Lower case numbers are not significant. 4.552 = 3 s.f.

I. When taking logarithms, such as for pH, the number of digits to the right of the decimal in the log is equal to the number of significant figures in the value which the log is taken of. For example: -log 0.012 = 1.91

Rules involving Calculations:

Rule 1: MULTIPLICATION/DIVISION (Powers & roots): The answer must be rounded off to the number of significant figures which are the same as that of the least significant digit value used in the calculation.

(0.0267) X (3.1) = 0.083

Rule 2: ADDITION/SUBTRACTION: The precision (places) of the answer must be the same as the least precise number used in the calculations. For example, the thousandths place is more precise that the hundredths place.

0.664 27.6 3.5 *Note: Addition can increase and

-0.65_ +31._ +8.3 subtraction can decrease the

0.01 58. 11.8 number of significant figures.

AVERAGING: The average result must contain the same precision (expressed to the same place) as the component values being averaged.

36.2 + 36.7 + 36.4 = 109.3 avg. = 109.3/3 = 36.4 *can only be to tenths place

in this case. Rule 2 is overridden when averaging.
 
 

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