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Introductory Physics Homework Help
Approximating Answers When Exact Numbers Are Involved
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[QUOTE="Steve4Physics, post: 6837510, member: 681522"] You’ve already had a couple of good replies from [USER=493650]@PeroK[/USER] and [USER=192687]@kuruman[/USER]. But since I’ve already written this... 9.81m/s² is typically used when a precision of 3 sig. figs. Is required. But 9.80m/s² is perfectly acceptable - the value of g varies with geographical location. It is common practice to ‘relax’ the rules and allow final answers to have one (but no more than one) extra significant figure. Your example (using g=9.8m/s²) is a case in point. If I marked this for an exam’ (when I used to do such things), I would accept either 637N or 640N. ____________ A few other thoughts… It the calculated value is then used in subsequent steps, the unrounded value should be used in these steps. Rounding the answer to 640 N is correct. However, in this particular case, the trailing zero creates ambiguity: ‘640 N’ could represent (640±10)N or (640±1) N! You would need to write 6.4x102N to avoid the ambiguity. It’s not a good system. Using g=9.8m/s²: -the implied minimum possible weight of the bucket is 64.95 * 9.75 = 633 N -the implied maximum possible weight of the bucket is 65.05 * 9.85 = 641 N So, the final value is implied to be between 633N and 641N. A more sophisticated approach would be use the explicit uncertainty of each value (e.g. m = (65.00±0.05)kg). An ‘error propagation’ technique would then be used to calculate the uncertainty of the result of the calculation. This is probably not required at the level you are currently working. Happy 2023!Edit - typos [/QUOTE]
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Approximating Answers When Exact Numbers Are Involved
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