Significant Figure
By Lorenz Manalad
“Significant Figures”
What Significant Figures Are?
The significant figures (also called significant digits) of a number are those digits that carry
meaning contributing to its precision. This includes all digits except:
• leading and trailing zeros where they serve merely as placeholders to indicate the scale of
the number.
• spurious digits introduced, for example, by calculations carried out to greater accuracy than
that of the original data, or measurements reported to a greater precision than the
equipment supports
The rules for identifying significant digits when writing or interpreting numbers are as follows:
• All non-zero digits are considered significant. For example, 91 has two significant digits
(9 and 1), while 123.45 has five significant digits (1, 2, 3, 4 and 5).
• Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12
has five significant digits: 1, 0, 1, 1 and 2.
• Leading zeros are not significant. For example, 0.00052 has two significant digits: 5 and
2.
• Trailing zeros in a number containing a decimal point are significant. For example,
12.2300 has six significant digits: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only
six significant digits (the zeros before the 1 are not significant). In addition, 120.00 has
five significant digits. This convention clarifies the accuracy of such numbers; for 2
example, if a result accurate to four decimal places is given as 12.23 then it might be
understood that only two decimal places of accuracy are available. Stating the result as
12.2300 makes clear that it is accurate to four decimal places.
• The significance of trailing zeros in a number not containing a decimal point can be
ambiguous. For example, it may not always be clear if a number like 1300 is accurate to
the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or
if it is only shown to the nearest hundred due to rounding or uncertainty. Various
conventions exist to address this issue… However, these conventions are not universally
used, and it is often necessary to determine from context whether such trailing zeros are
intended to be significant.
· Addition and Subtraction
When measured quantities are used in addition or subtraction, the uncertainty is determined by the absolute uncertainty in the least precise measurement (not by the number of significant figures). Sometimes this is considered to be the number of digits after the decimal point.
Example
32.01 m
5.325 m
12 m
Added together, you will get 49.335 m, but the sum should be reported as '49' meters.
· Multiplication and Division
When experimental quantities are mutiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. If, for example, a density calculation is made in which 25.624 grams is divided by 25 mL, the density should be reported as 1.0 g/mL, not as 1.0000 g/mL or 1.000 g/mL.
Rounding Numbers
There are different methods which may be used to round numbers. The usual method is to round numbers with digits less than 5 down and numbers with digits greater than 5 up (some people round exactly 5 up and some round it down).
Example:
If you are subtracting 7.799 g - 6.25 g your calculation would yield 1.549 g. This number would be rounded to 1.55 g, because the digit '9' is greater than '5'.
In some instances numbers are truncated, or cut short, rather than rounded to obtain appropriate significant figures. In the example above, 1.549 g could have been truncated to 1.54 g.
By Lorenz Manalad
“Significant Figures”
What Significant Figures Are?
The significant figures (also called significant digits) of a number are those digits that carry
meaning contributing to its precision. This includes all digits except:
• leading and trailing zeros where they serve merely as placeholders to indicate the scale of
the number.
• spurious digits introduced, for example, by calculations carried out to greater accuracy than
that of the original data, or measurements reported to a greater precision than the
equipment supports
The rules for identifying significant digits when writing or interpreting numbers are as follows:
• All non-zero digits are considered significant. For example, 91 has two significant digits
(9 and 1), while 123.45 has five significant digits (1, 2, 3, 4 and 5).
• Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12
has five significant digits: 1, 0, 1, 1 and 2.
• Leading zeros are not significant. For example, 0.00052 has two significant digits: 5 and
2.
• Trailing zeros in a number containing a decimal point are significant. For example,
12.2300 has six significant digits: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only
six significant digits (the zeros before the 1 are not significant). In addition, 120.00 has
five significant digits. This convention clarifies the accuracy of such numbers; for 2
example, if a result accurate to four decimal places is given as 12.23 then it might be
understood that only two decimal places of accuracy are available. Stating the result as
12.2300 makes clear that it is accurate to four decimal places.
• The significance of trailing zeros in a number not containing a decimal point can be
ambiguous. For example, it may not always be clear if a number like 1300 is accurate to
the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or
if it is only shown to the nearest hundred due to rounding or uncertainty. Various
conventions exist to address this issue… However, these conventions are not universally
used, and it is often necessary to determine from context whether such trailing zeros are
intended to be significant.
· Addition and Subtraction
When measured quantities are used in addition or subtraction, the uncertainty is determined by the absolute uncertainty in the least precise measurement (not by the number of significant figures). Sometimes this is considered to be the number of digits after the decimal point.
Example
32.01 m
5.325 m
12 m
Added together, you will get 49.335 m, but the sum should be reported as '49' meters.
· Multiplication and Division
When experimental quantities are mutiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. If, for example, a density calculation is made in which 25.624 grams is divided by 25 mL, the density should be reported as 1.0 g/mL, not as 1.0000 g/mL or 1.000 g/mL.
Rounding Numbers
There are different methods which may be used to round numbers. The usual method is to round numbers with digits less than 5 down and numbers with digits greater than 5 up (some people round exactly 5 up and some round it down).
Example:
If you are subtracting 7.799 g - 6.25 g your calculation would yield 1.549 g. This number would be rounded to 1.55 g, because the digit '9' is greater than '5'.
In some instances numbers are truncated, or cut short, rather than rounded to obtain appropriate significant figures. In the example above, 1.549 g could have been truncated to 1.54 g.