Significant Figures
2
SIGNIFICANT FIGURES The number of significant figures in a numerical quantity equals the number of digits in the quantity less all zero digits that are used to fix the position of the decimal point. For example: 147 has 3 significant figures; 147,64 has 5 significant figures; 2,1 has 2 significant figures; 1013 has 4 significant figures; 1.007 has 4 significant figures; 17.710 has 5 significant figures; 0.021 has 2 significant figures; 1320 has either 3 or 4 significant figures, depending on whether or not the zero digit is used only to fix the position of the implied decimal point which follows it. A numerical value should carry all certain digits plus the first digit that is doubtful. If, for example, the first four digits of the value 137.824 are certain and the last two digits are doubtful, the value should be expressed to only five significant figures, i.e., 137.82 (1, 3, 7, and 8 are certain, 2 is doubtful). The number of significant figures in a directly measured quantity is not usually difficult to determine, as it essentially depends on the least count of the instrument used. For example, if a distance is measured with a tape graduated in centimeters, with estimation to milimeters, and a reading of 462.513 m is taken, the first five digits are certain, the sixth significant figures. The number of significant figures in a numerical quantity is reduced by rounding off. The least error will be caused if rounding off is done according to the following rules : 1. If k significant figures are required, discard all digits to the right of the (k + 1)th digit. 2. Examine the (k +1)th digit. a. If it is 0 to 4, discard it; e.g., 12.34421 is rounded off to four significant figures as 12.34. b. If it is 6 to 9, discard it and increase the kth digit by one; e.g., 1.376 is rounded off to three significant figures as 1.38.
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Transcript of Significant Figures
SIGNIFICANT FIGURES
The number of significant figures in a numerical quantity equals the number of digits in the quantity less all zero digits that are used to fix the position of the decimal point. For example:
147 has 3 significant figures;
147,64 has 5 significant figures;
2,1 has 2 significant figures;
1013 has 4 significant figures;
1.007 has 4 significant figures;
17.710 has 5 significant figures;
0.021 has 2 significant figures;
1320 has either 3 or 4 significant figures, depending on whether or not the zero digit is used only to fix the position of the implied decimal point which follows it.
A numerical value should carry all certain digits plus the first digit that is doubtful. If, for example, the first four digits of the value 137.824 are certain and the last two digits are doubtful, the value should be expressed to only five significant figures, i.e., 137.82 (1, 3, 7, and 8 are certain, 2 is doubtful).
The number of significant figures in a directly measured quantity is not usually difficult to determine, as it essentially depends on the least count of the instrument used. For example, if a distance is measured with a tape graduated in centimeters, with estimation to milimeters, and a reading of 462.513 m is taken, the first five digits are certain, the sixth significant figures.
The number of significant figures in a numerical quantity is reduced by rounding off. The least error will be caused if rounding off is done according to the following rules :
1. If k significant figures are required, discard all digits to the right of the (k + 1)th digit.2. Examine the (k +1)th digit.
a. If it is 0 to 4, discard it; e.g., 12.34421 is rounded off to four significant figures as 12.34.b. If it is 6 to 9, discard it and increase the kth digit by one; e.g., 1.376 is rounded off to
three significant figures as 1.38.c. If it is 5 and the kth digit is even, discard it; e.g., 12.345 is rounded off to four significant
figures as 12.34.d. If it is 5 and the kth digit is odd, discard it and increase the kth digit by one; e.g., 12.3435
is rounded off to five significant figures as 12.344
The number of significant figures is not so easily determined in a quantity obtained by computation as it is in a directly measured quantity. There are, however, some general rules that can be applied with reasonable effectiveness. The two most important rules deal with the arithmetic operations, addition (or subtraction) and multiplication (or division).
In the process of addition, the sum should be rounded off to the number of decimal places that is least in the quantities being added. For example, the sum.
165.21
149.7
65.495
2. 2167
382.6217
Should be rounded off to 382.6 because 149.7 is expressed to only one decimal place.
In multiplication, the number of significant figures in the product should equal the number significant figures, exact numerical factors excluded. For example :
2.15 x 11.1234 = 23.9
2(2.15 x 11.1234) = 47.8 (2 is an exact factor)
In each case, the number of significant figures (3) in 2.15 decides the number of significant figures in the product.
In computations with a large number of arithmetic operations, it is good practice to carry one significant figures throughout, then round off after the computations are completed.
