Review of Introductory Mathematics
This chapter presents the concept of significant digits and the application of
significant digits in a calculation.
DETERMINE the number of significant digits in a given
Given a formula, CALCULATE the answer with the
appropriate number of significant digits.
Calculator Usage, Special Keys
Most calculators can be set up to display a fixed number of decimal places. In doing so,
the calculator continues to perform all of its internal calculations using its maximum
number of places, but rounds the displayed number to the specified number of places.
To fix the decimal place press the INV key and the number of the decimal places
desired. For example, to display 2 decimal places, enter INV 2.
When numbers are used to represent a measured physical quantity, there is uncertainty associated
with them. In performing arithmetic operations with these numbers, this uncertainty must be
taken into account. For example, 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 by a
survey which is known to be exact to the nearest 1/1000 of a mile? In order to take this
uncertainty into account, we have to realize that we can be only as precise as the least precise
number. Therefore, the number of significant digits must be determined.
Suppose the example above is used, and one adds 3.872 miles determined by survey to 2.2 miles
obtained 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. Since all we know
about the 2.2 miles is that it is more than 2.1 and less than 2.3, we certainly dont know the sum
to any better accuracy. A single digit to the right is written to denote this accuracy.