Significant figures addition/subtraction rounding? I thought you round to the same place as the number with the addend with the least precision. For example, if you had $25.63+ 42.3$ the answer would be rounded to the tens place ($67.9$).
However, my chemistry teacher just said that it would be rounded to the same place as the number with the least places after the decimal point. Is this true?
For example, if I added 100+32, would it be rounded to the ones place (because there are no digits after the decimal point) or would it be rounded to the hundreds place (because 100 has the lowest precision, with its only sigfig in the hundreds place)?
Thanks.
 A: If your example had been $$0.26 (2\text{ sig.fig. or }2 \text{ decimal places})+42.3 (3\text{ sig.fig. or }1 \text{ decimal place})$$ your chemistry teacher would have advised an answer of $42.6 (1 \text{ decimal place})$.
As for adding $100$, it depends on how accurately this was measured.  Was it rounded to the nearest $100$, nearest $10$, nearest $1$ or nearest $0.1$? 
A: Rounding rules are pretty arbitrary,
with their goal being to
lose as little information as possible.
The results also depend on
how accurate the inputs are.
For example,
for "100+32",
if nothing is stated about the inputs,
I would assume that
the answer is 132,
since I would assume that
the 100 is exact.
If the inputs are not exact,
there are either implicit
or explicit error bounds.
For example,
if that 100 were known
to two figures,
the units digit would
be in doubt,
and you could write it
as "$100\pm 5$"
(or "105$\pm$5").
With regards to what
your instructor said,
they said
"after the
decimal point."
This assumes that
all the figures to the
left of the decimal point
are correct.
There is a lot more that
I could say,
but that's enough for now.
