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I was taught to use the same number of significant figures in my answer as the piece of data with the lowest number of significant figures, so I was a bit confused when the solutions manual for this problem stated the answer as 2.45ms^-2.

Problem: The acceleration due to gravity at the earth's surface is 9.8ms-2. Calculate the acceleration due to gravity on a planet which has the same mass and twice the radius as the earth.

Here the piece of data with the lowest number of significant figures is 9.8ms-2 (2 sig fig), so shouldn't the answer be 2.5ms-2 and not 2.45ms-2 ?

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    $\begingroup$ So what if the person providing that answer simply wasn't following that rule? $\endgroup$
    – Name
    Commented May 6, 2015 at 11:52
  • $\begingroup$ @Name: But they state it at the start of their book! $\endgroup$
    – user45220
    Commented May 6, 2015 at 11:57
  • $\begingroup$ Ohm stated a law of constant electrical resistance, but as a human he did not have a constant resistance himself. People don't always follow their own rules. =) $\endgroup$
    – Name
    Commented May 6, 2015 at 17:59
  • $\begingroup$ @Name Haha good one, but I can't resist (pun intended) pointing out that Ohm's law applies to a very special situation, whereas the rule given in the book is said to apply to "any physics calculation" $\endgroup$
    – user45220
    Commented May 6, 2015 at 18:43
  • $\begingroup$ More on significant figures. $\endgroup$
    – Qmechanic ♦
    Commented Apr 17, 2016 at 14:14

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I think the error arises from the fact that it is common to use $$9.80 m/s^2$$ Perhaps this is what was meant.

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  • $\begingroup$ So as it is stated in the book (i.e. "9.8ms-2") does it mean the answer should be "2.5ms-2"? Thanks $\endgroup$
    – user45220
    Commented May 6, 2015 at 11:46
  • $\begingroup$ @user45220 yes, you should have been right $\endgroup$
    – Jimmy360
    Commented May 6, 2015 at 11:51

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