MANIPULATION OF NUMERICAL DATA
A. EXACT NUMBERS (i.e. numbers obtained by counting or defined fractions [math]) are considered
perfectly precise: thus neither are they rounded nor do the rules for approximate numbers apply.
B. APPROXIMATE NUMBERS (i.e. numbers obtained by measurement [science]) are subject to the
following rules:
1 i) SIGNIFICANT DIGITS
To determine the number of significant digits in a number:
a) All the digits from 1 to 9 including any zeros between them are significant.
b) The zeros preceding the first non-zero digit are not significant.
c) The zeros at the end of a number are not significant if there is no decimal in the number.
1 ii) STANDARD FORM or SCIENTIFIC NOTATION
To represent the number of significant digits in very large or very small numbers:
a) Disregard the magnitude of the number and write down the correct number of significant
digits beginning from the left.
b) Insert a decimal point so that only one digit remains to the left.
c) Multiply the number by a power of ten to give it the correct magnitude.
#.####  10x
1 iii) ROUNDING OF DATA
a) When the first digit discarded is less than 5, the last digit retained should not be changed.
b) When the first digit discarded is greater than 5, or if it is a five followed by at least one
digit other than zero, the last figure retained should be increased by one unit.
c) When the first digit discarded is exactly 5 (no following digits), the last digit retained
should be rounded to the nearest even digit, if necessary.
Operations
1.
Addition and subtraction. The result after rounding the answer should be as precise as the
least precise of the numbers used. (with respect to the number of digits to the right of the
decimal)
2.
Multiplication and division. The result after rounding the answer should contain as many
significant digits as are contained in the number used with the fewest significant digits.
So the rules are:
a) Determine the measured number with the fewest significant digits. (see 1 i above)
b) Carry all multiplication and division operations to at least one more significant digit than
in this number.
c) Round off your answer to the same number of significant digits as in this number.
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Significant Digits.wpd
SIGNIFICANT DIGITS EXAMPLES
To determine the number of significant digits in a number:
a) All the digits from 1 to 9 including any zeros between them are significant.
b) The zeros preceding the first non-zero digit are not significant.
c) The zeros at the end of a number are not significant if there is no decimal in the number.
Example
SigDigs
Scientific Notation
123
1230
12300
0.000445
0.00342
1.34
12033
20
4500
4500.
4500000
0.034400
0.03440000
0.04005
500
500.
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Significant Digits.wpd