On Apr 10 , at 9:07 AM, Stan Jakuba wrote:
In calculations, the number with the fewest of sig. dig's
determines the outcome. To illustrate, 17.5 m in 2 s is 9 m/s,
whereas 17.5 m
in 2.00 s is 8.75 m/s.
That rule applies only to multiplication and division (including
square, square roots, etc). It does not apply to addition or
subtraction.
In adding a set of figures, the result is rounded to the same decimal
place as the decimal place of the number with the fewest decimal
places, e.g.
When adding 123.45 + 32.789 + 356.7 + 2.7255
the calculator result if ALL the digits are used would be
515.6645
However, that answer cannot possibly be good to four decimal places
since one of the numbers being added is only good to one decimal place
(the number 356.7). Thus the answer should be rounded to one decimal
place giving the final result of
515.7
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
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SImplification Begins With SI.
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PS
If we wished to save a little time by not entering all the digits when
some of them are going to get rounded away anyhow, we could consider
that the result will need to be rounded to one decimal place and
therefore we COULD round all the numbers to one decimal place before
adding the figures. However, that can lead to small rounding errors
and a better procedure is to keep one extra digit in each number, add
them, then round off the extra digit in the answer.
Doing that in the above leads to using
123.45 +32.79 + 356.7 + 2.73
and getting an unrounded answer of
515.67
which, when rounded off to one decimal place, gives
515.7
exactly as is obtained with the longer process of keeping all the
decimal places.
(In this example, rounding off all values to one decimal place before
adding also gives the same result, but it sometimes does not.)
