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Rounding Off After Addition and Subtraction
When adding and subtracting, we round off the answer to the same
number of decimal places that are in the number with the fewest decimal
places. Notice, I said decimal places, not significant digits.
.123
+ .421012
.544 |
With decimal fractions this
can be pretty straight forward, as in the first case here (.123 + .421012). Notice that
the 012 part is lost in the final answer. There are no corresponding numbers for them to
be added to. We don't know what comes after the .123. |
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.123???
+ .421012
.544??? |
We could think of the number as .123???, then
the 012 plus ??? equals ???. Since we don't know what the 012 would be added to, we have
to leave them off. |
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.123
+ .000012
.123 |
Sometimes this can be a little bit troublesome
as in the next case (.123 + .000012) where the entire second number is lost because the
imprecision and the uncertainty of the .123 is larger than the number to be added.
Consequently, it doesn't get represented. |
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4100
+ 304
4400 |
In this last case we will presume those zeros
not to be significant. When 4,100 is added to 304, we get becomes 4,400. The four in the
ones place is not shown. We are not really sure what it is being added to. If we put down
4,404 as an answer, that would imply that we knew that those zeros in the 4,100 were
significant digits. If we do know that, then the answer is 4,404. Since we don't know, the
last four gets lost in the uncertainty. |
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