Comments on: Of Approximation And That Granny On A Trishaw

By: TJK

TJK — Fri, 15 Oct 2010 13:27:12 +0000

Actually for 1.2345678 (exact)

I feel i have a safer way (I did it for more than once for exams)

1.2345678 (exact) which is approx. to 1.23 (3 s.f.)

By: Miss Loi

Miss Loi — Fri, 15 Oct 2010 04:00:06 +0000

Your question seems to have ignited one of the controversies of the century as far as O level AMaths go :P To be absolutely honest, when Miss Loi made her "clear as day: to the nearest cent" remark she was referring to answers in the Money & Personal Finance topic under the Arithmetic chapter in EMaths, where students are specifically tested on the transactions and values of money, and hence non-exact answers should be left to the nearest cent. The 2008 AMaths Paper 2 Q1, however, is actually a question on Logarithmic and Exponential functions and hence Miss Loi did the calculations and left the answer, in her usual way for such questions, in 3 sig. fig. Yes it's an assumption and so in a quest to get a better consensus, she decided to 飞鸽传书 (via her students) this query to some teachers and at the same check some of the standard TYS solutions. And the result is ...

ShingLee TYS says to the nearest cent (2 d.p.)
Dyna TYS says 3 sig. fig.
5 out of 6 teachers say it's to the nearest cent (since it's money)
However, the last teacher was reported to have pulled out the Imperial Edict aka 圣旨 aka Cambridge Marker's Report following which the whole class ~~knelt down to~~ see that the final answer was left in 3 sig. fig.!

As such, Miss Loi thinks she'll leave that particular answer in 3 sig. fig. for now. Did you ask your cher's opinion on this?

By: Aaron

Aaron — Tue, 12 Oct 2010 07:22:40 +0000

Thanks for the help!

Quote:
" ... answers in money should be rounded off to the nearest cent and not 3 significant figures e.g. $245.67 and not $246 (3sf)?"

This should be as clear as day by now: Unless stated otherwise, money should be rounded off to the nearest cent e.g. $100.00

I refer to the O level 2008 Additional Mathematics Suggested Solutions
http://www.exampaper.com.sg/wp-content/uploads/gce-o-level-2008-amaths-4038-paper-2-solutions.pdf

For question 1 (ii), you rounded off your "Value after 18 months" to 3 significant figures. Should the answer be $2529.80 (corrected to nearest cent)?

Could the answer be because when in cents, it depends on the accuracy of the 'p' value which is approximated? Which means that since the 'p' value was already rounded to a number of significant figures (preferred by the candidate but not less than 4), it is not smart to round it to the nearest cent as it means 6 significant figures when the value of 'p' was already rounded off to 5 sf?

By: Miss Loi

Miss Loi — Sun, 10 Oct 2010 14:41:13 +0000

A couple of question was asked here but Miss Loi finds it more appropriate to reply here, since they deal with the topic of this blog post: "... is it true that candidates should leave final answers (other than in degrees) to 3 significant figures ONLY if the answer is not exact. E.g. 74.5 / 4, do we leave our final answer as 18.625 since it is exact?"

This has been a longstanding debate amongst anxious students, teachers and schools every year but the straightforward answer is 
yes - all exact answers should be left as they are i.e. in the exact number of decimal places.

The not-so-straightforward scenario would be what if your "exact" answer happens to be exactly 1.2345678, as mentioned at the end of this blog post? A certain school even once ascertained that "the answer is deemed to be exact if it doesn't fill up the whole of the calculator's screen". But calculators are created different with different number of digits!

Granted these are freak cases, perhaps it's best to leave the final  answer with its full compliment of decimal places or in fraction form, with the remark 'exact' next to it just to convince the examiner that you know what you're doing, should you encounter something like this. Anyone disagree?

" ... use at least 4 significant figures to do working, and if the working includes figures that have been rounded off to 4sf, the final answer should be corrected to 3sf even if it appears as a fraction which is exact?"

Yes, the accuracy of your final answer would have been affected by rounding off the intermediate values in your working. So as a result, your final answer is non-exact.

" ... answers in money should be rounded off to the nearest cent and not 3 significant figures e.g. $245.67 and not $246 (3sf)?"

This should be as clear as day by now: Unless stated otherwise, money should be rounded off to the nearest cent e.g. $100.00

Don't short-change yourself!

By: happious

happious — Mon, 08 Mar 2010 15:55:04 +0000

what is the marking scheme for paper 1 and 2?
are marks awarded for workings in paper 1?

By: Miss Loi

Miss Loi — Fri, 24 Jul 2009 04:35:18 +0000

If your dog looks like a cat
You may need to change your specs :p
And if maths is hard to understand
Maybe a sexy maths tutor can lend a hand

By: plankton

plankton — Thu, 23 Jul 2009 13:51:51 +0000

In such unanticipated situation, one should rebel, flaunt the rules, and shock the teacher by penning a heart-felt poem instead!

Roses are red, violets are blue.
I have a dog, but it looks like a cat.
It's very confusing, very much like maths.

Heh :p

By: Miss Loi

Miss Loi — Thu, 23 Jul 2009 05:30:32 +0000

How many significant figures does 87000 contain? http://bit.ly/NPwLu