This
chapter presents the concept of significant digits and the application of
significant digits in a calculation.
EO
1.8DETERMINE the number of significant
digits in a given number.
EO1.9 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.
INV
key
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.
Significant Digits
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 don't know the sum to any better
accuracy. A single digit to the right is written to denote this accuracy.
Both the precision of numbers and the number of
significant digits they contain must be considered in performing arithmetic
operations using numbers which represent measurement. To determine the number
of significant digits, the following rules must be applied:
Rule 1: The
leftmost nonzero digit is called the most significant digit.
Rule 2: The rightmost
nonzero digit is called the least significant digit except when there is a
decimal point in the number, in which case the rightmost digit, even if it is
zero, is called the least significant digit.
Rule 3: The number
of significant digits is then determined by counting the digits from the least
significant to the most significant.
Example:
In the number 3270, 3 is the most significant digit, and 7
is the least significant digit.
Example:
In the number 27.620, 2 is the most significant digit, and
0 is the least significant digit.
When adding or subtracting numbers which represent
measurements, the rightmost significant digit in the sum is in the same
position as the leftmost least significant digit in the numbers added or
subtracted.
Example:
15.62 psig + 12.3 psig = 27.9 psig
Example:
401.1 + 50 = 450
Example:
401.1+50.0=451.1
When multiplying or dividing numbers that represent
measurements, the product or quotient has the same number of significant digits
as the multiplied or divided number with the least number of significant
digits.
Example:
3.25 inches x 2.5 inches = 8.1 inches squared
Summary
The important information from this chapter is summarized
below.
Significant
Digits Summary
Significant digits are determined by counting the number
of digits from the most significant digit to the least significant digit.
When adding or subtracting numbers which represent
measurements, the rightmost significant digit in the sum is in the same
position as the leftmost significant digit in the numbers added or subtracted.
When multiplying or dividing numbers that represent
measurements, the product or quotient has the same number of significant digits
as the multiplied or divided number with the least number of significant
digits.
