how many significant figures go into "results to be reported"? When writing # +/- #, is the second # always written to only 1 significant figure?
The first q is not answerable. Generally, one puts all sig figures in numbers. On the second question, no.
It is customary to include two significant digits in the error.
The number of significant figures in a "result to be reported" typically depends on the precision of the measurement or calculation. In general, you want to report as many significant figures as you have confidence in based on the precision of your measurements or the accuracy of your calculations.
When writing a result in the form of "# +/- #," the second number after the plus/minus sign (the uncertain digit or uncertainty) is typically written to one significant figure. This is a common convention that indicates the level of precision or uncertainty of the result.
To determine the number of significant figures in a result, follow these steps:
1. Identify the uncertain digit: Look at the value given after the plus/minus sign in the result. This digit represents the level of uncertainty or precision.
2. Count the number of significant figures before the uncertain digit: Start from the leftmost non-zero digit and count all the digits, including zeros, until you reach the uncertain digit. Trailing zeros after the decimal point are significant.
3. Write the result with the appropriate number of significant figures: Keep all the significant figures identified in step 2, and round the uncertain digit according to the rules of significant figures.
For example, if the result is 5.789 +/- 0.01:
- The uncertain digit is 0.01, written to one significant figure.
- The significant figures before the uncertain digit are 5, 7, 8, and 9.
- Therefore, the result with the appropriate number of significant figures is 5.79 +/- 0.01.
Remember to always use the correct number of significant figures when reporting your results, as it reflects the precision of your measurement or calculation.