Chapter 1
Relationships
1.6 What's Significant about a Digit?
1.6.2 Accuracy of Measurements
In Section 1.3 we described several dichotomies by which we can sort our functions into various conceptual categories. For example, the position of a moving object is a real function of time that has an exact value at every instant of time — but we may know only an observable approximation to this exact value and only at selected instants of time. That is, we may have only a finite list of numbers, such as the distance numbers in the table in Checkpoint 2 of Section 1.1. These numbers are necessarily limited in significance by the precision of the device that made the measurements, and it would be silly to expect that we can ever gain additional significance by doing calculations on the numbers.
Suppose a population of 240,000,000 people grows by 2% per year for three years. What will the population be at the end of the three years? (Use the pop-up calculator to help with the calculation -- you will find the "memory" useful for this task.)
| Moral of Activity 1 Calculation steps never add significant digits, so don't always believe all the digits you see on your computer. |
