Solving Significant Digit Problems with Varying Order of Magnitude

[Irid]

I have reasons to believe that my question asks to write the answer with 3 significant digits (i.e. the given numbers are with 3 digits). But there are several figures to be worked out, so I list them (for example):

3.45
3.89
7.90
...
10.23 or 10.2 (or even 10.20)?

The problem is that the order of magnitude of the answers varies and I don't know what to do: write 4 significant digits (although I should know only 3) or stick with only 3, but then the number digits after the decimal point is different.

 

[Defennder]

It should be 10.2 10.20 appears to imply that you measured down to 100th decimal place of accuracy. 10.23 is 4 sig fig.

 

[baba89]

I understand the importance of accurately representing data and maintaining the appropriate number of significant digits. In this case, it is important to first determine the level of precision required for your calculations. If your given numbers are only accurate to three significant digits, then it would be appropriate to round your final answers to three significant digits as well.

When dealing with numbers of varying orders of magnitude, it is important to maintain the same level of precision throughout your calculations. This means that you should not add or subtract any numbers with more significant digits than what is given in your original data. For example, if your given numbers are only accurate to three significant digits, you should not add a number with four or more significant digits in your calculations.

In regards to your question about the final answer of 10.23 or 10.2, it would be appropriate to round the final answer to 10.2 to maintain consistency with the given data of three significant digits. However, if you are unsure about the accuracy of your calculations, it would be best to err on the side of caution and round to the final answer to 10.20 to maintain the appropriate number of decimal places.

In summary, when solving significant digit problems with varying orders of magnitude, it is important to stick to the level of precision given in your original data and maintain consistency throughout your calculations. By doing so, you can ensure accurate and reliable results.