what are the errors in the measured values g=9.910 m/s^2 amd 9.805? true value 9.797 for 9.910 i got 0.113 and for 9.805 i got 0.008. i know i need for significant figures but i got three in my answer. so what do i do?
When you determine s.f. in subtraction (and addition), you are allowed places to the right of the decimal that equals the least precise value. In this case you are allowed 3 places and you have 3 places. You can't have 4. Your answers are right.
To determine the errors in the measured values, you need to calculate the absolute difference between each measured value and the true value.
For the first measured value, g = 9.910 m/s^2, the absolute difference would be:
|9.910 - 9.797| = 0.113 m/s^2
For the second measured value, g = 9.805 m/s^2, the absolute difference would be:
|9.805 - 9.797| = 0.008 m/s^2
Now, regarding your concern about the significant figures, it's always a good practice to have your answer rounded to the appropriate number of significant figures based on the least precise measurement. In this case, the least precise measurement is 9.805 m/s^2, which has four significant figures.
To adhere to significant figure rules, you can round your answers as follows:
For the first measurement: 0.113 m/s^2 can be rounded to 0.11 m/s^2 (2 significant figures based on the least precise measurement).
For the second measurement: 0.008 m/s^2 can be rounded to 0.0080 m/s^2 (3 significant figures based on the least precise measurement).
So, your final rounded errors would be 0.11 m/s^2 and 0.0080 m/s^2, respectively.