Читать книгу Physics I For Dummies - Steven Holzner - Страница 36

When you do calculations, you often need to round your answer to the correct number of significant digits. If you include any more digits, you claim a precision that you don’t really have and haven’t measured.

For example, if someone tells you that a rocket traveled 10.0 meters in 7.0 seconds, the person is telling you that the distance is known to three significant digits and the seconds are known to two significant digits (the number of digits in each of the measurements). If you want to find the rocket’s speed, you can whip out a calculator and divide 10.0 meters by 7.0 seconds to come up with 1.428571429 meters per second, which looks like a very precise measurement indeed. But the result is too precise — if you know your measurements to only two or three significant digits, you can’t say you know the answer to ten significant digits. Claiming as such would be like taking a meter stick, reading down to the nearest millimeter, and then writing down an answer to the nearest ten-millionth of a millimeter. You need to round your answer.

The rules for determining the correct number of significant digits after doing calculations are as follows:

 When you multiply or divide numbers: The result has the same number of significant digits as the original number that has the fewest significant digits. In the case of the rocket, where you need to divide, the result should have only two significant digits (the number of significant digits in 7.0). The best you can say is that the rocket is traveling at 1.4 meters per second, which is 1.428571429 rounded to one decimal place.

 When you add or subtract numbers: Line up the decimal points; the last significant digit in the result corresponds to the right-hand column where all numbers still have significant digits. If you have to add 3.6, 14, and 6.33, you’d write the answer to the nearest whole number — the 14 has no significant digits after the decimal place, so the answer shouldn’t, either. You can see what we mean by taking a look for yourself:

 When you round the answer to the correct number of significant digits, your answer is 24.

When you round a number, look at the digit to the right of the place you’re rounding to. If that right-hand digit is 5 or greater, round up. If it’s 4 or less, round down. For example, you round 1.428 up to 1.43 and 1.42 down to 1.4.