While numbers are used to represent a measured physical quantity, there is uncertainty related with them. In performing arithmetic operations along with these numbers, this uncertainty must be taken within account. For instance, an automobile odometer measures distance to the nearest 1/10 of a mile. How can a distance measured on an odometer be added to a distance measured through a survey that is known to be exact to the nearest 1/1000 of a mile? In sequence to take this uncertainty into account, we have to realize that we could be only as precise as the least precise number. Thus, the number of significant digits must be determined.
Assume the example above is used, and one adds 3.872 miles determined through survey to 2.2 miles acquired from an automobile odometer. This would sum to 3.872 + 2.2 = 6.072 miles, but the last two digits are not reliable. Thus the answer is rounded to 6.1 miles. Because all we know about the 2.2 miles is in which it is more than 2.1 and less than 2.3, we certainly don't know the sum to any better accuracy. A single digit to the right is written to imply this accuracy.
Both the precision of numbers and the number of significant digits they hold must be considered in performing arithmetic operations using numbers that represent measurement. For determine the number of significant digits, the subsequent rules must be applied:
Rule 1: The left-most non-zero digit is known as the most significant digit.
Rule 2: The right-most non-zero digit is known as the least significant digit except while there is a decimal point in the number, in that case the right-most digit, even if it is zero, is known as the least significant digit.
Rule 3: The number of significant digits is then determined through counting the digits from the least significant to the most significant.