### 1.2 Rounding & Calculators

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• Math Help

The phrase "garbage in, garbage out" is often used by computer programmers. Basically, it means that if the information you input is wrong (garbage), then the resulting output will also be wrong (garbage). This same principle applies to any type of calculation.

Here is an example. Suppose someone claims that the population of Chicago is 2,725,418 and the population of San Francisco is 803,548. Such a claim has to be "garbage." No one could know these populations with this amount of accuracy. So, if you use these numbers to claim that the combined population of the two cities is

your claim is also "garbage." A more reasonable claim would be to say that the populations are about 2.7 million and 0.8 million, implying that the combined population is about 3.5 million.

• Consumer Suggestion

Ever wonder how each U.S. state's population is determined? Check out the U.S. Census Bureau.

• Checkpoint Solution

In rewriting these statements, remember that when you are communicating significant digits, you have two considerations.

1. Don't list more digits than you know are correct.
2. Don't list more digits than your audience needs.

1. Original Statement: The weight of an athlete is 213.6 pounds. Perhaps this statement could be valid, provided it was made minutes before a wrestling match, in which exact weight is important. In most contexts, however, this level of accuracy is inappropriate for listing a person's weight. After all, in any 24-hour period weight can easily vary by 2 or 3 pounds.

Rewritten Statement: The weight of an athlete is about 215 pounds.

2. Original Statement: The record time for a 100-meter dash is 9.58 seconds. For many years, track events have commonly measured times to the nearest hundredth of a second. So, this statement does not need to be rewritten.
3. Original Statement: The distance between Earth and the Sun is 92,955,819 miles. This statement is in the field of science, so precise accuracy could be appropriate. Even so, when you think about the statement, you wonder what it means. Is it the distance between the centers or the surfaces? Moreover, Earth orbits the Sun in an elliptical path, not a circular path. So, the "distance" between Earth and the Sun is not constant. For this reason, the statement would be better rewritten.

Rewritten Statement: The distance between Earth and the Sun is about 93 million miles.

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