Significant figures question

Found 14th Jan

If 3.4 x 1.23 = 4.182

Obviously, if that were the only calculation the answer would be 4.2.

However, in multi-stage calculations, how would I carry the amount over? Would it be to the lowest number of significant figures +1 (4.18 or the higher number +1 (4.182)?

Thank you

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13 Comments

14th Jan

BODMAS. The sequence by which you treat the mathematical symbols

Brackets of Division Multiplication Addition Subtraction.

14th Jan

You should give the answer in at least as many sigfigs as the question, so 3 in your example. To keep things accurate use as many sigfigs in each stage until the end of the calculation.

14th Jan

BODMAS - there is no discrepancy in the initial sum is there? No brackets, no division - just a straight forward multiplication. Therefore the sigfigs are perhaps relevant to the question (we haven't seen the question in full perhaps) or relevant to the answer. If the answer is 4.182 then the 2 means it is rounded down to 4.18....

Happy to hear other view points, I did A level math but back in the day....!

14th Jan

you need significant figures + 1 as a minimum in the intermediaries for the final answer to be accurate, especially if you have lots of calculation cycles, but as randomuser states, use as many significant figures as you can for higher accuracy.

depending on the number of calculation iterations, large significant figures can still produce inaccuracy. i always use the maximum significant figures that the system will allow in the iterations.

14th Jan

Depends on how many significant figures it wants the answer in, the more you round the less precise the answer is

14th Jan

ccnp48 m ago
BODMAS. The sequence by which you treat the mathematical symbolsBrackets …BODMAS. The sequence by which you treat the mathematical symbolsBrackets of Division Multiplication Addition Subtraction.

Not sure what this is contributing.......

14th Jan

It's highly context dependant - it depends on what the trade-offs in terms of storage space and performance are and how much precision is useful in the answer.

14th Jan

Depends on if your rounding up or Down and that depends on which one is more desirable. New trust a man that uses the word average.

14th Jan

You would just round your answer, I’d never round the numbering in anything other then the output. Depending on what you are using it for you should always have the full significant figures and choose to round at the end!!

14th Jan

Oh dear. The question said '... multi stage calculations ....' and I, obviously incorrectly in your view, took that to mean a somewhat more complex sum. However, as is customary these days, I humbly acknowledge the correctness of your observation and that laxity of my incorrectness.

A proper exam question (pre 1980s and the mass dumbing down of education standards started by the C*ntservatives) would have included an instruction as to the number of significant places to which the calculation should be made.

I took did Os in 1972. Today, it probably awards marks for your PC contemplation the feelings of the places that have been rounded down (and sadly, many students could probably answer that with more gusto than calculate the answer).

14th Jan

9.999 for your apology. (You can round that up to the nearest whole number if you like)

Edited by: "Toptrumpet" 14th Jan

14th Jan

ccnp3 h, 40 m ago
Oh dear. The question said '... multi stage calculations ....' and I, …Oh dear. The question said '... multi stage calculations ....' and I, obviously incorrectly in your view, took that to mean a somewhat more complex sum. However, as is customary these days, I humbly acknowledge the correctness of your observation and that laxity of my incorrectness.A proper exam question (pre 1980s and the mass dumbing down of education standards started by the C*ntservatives) would have included an instruction as to the number of significant places to which the calculation should be made.I took did Os in 1972. Today, it probably awards marks for your PC contemplation the feelings of the places that have been rounded down (and sadly, many students could probably answer that with more gusto than calculate the answer).

Even students doing their “dumbed down” exam papers would have took the time to read the question and not just jumped right in ahead of themselves

Edited by: "Dannyrobbo" 14th Jan

15th Jan

When performing calculations the final answer should contain only as many significant figures as the number with the least number of significant figures. Keep at least one more digit during the calculations then round to the required number of significant figures for the final answer.

So answer would be 4.2, but if you are continuing you would use 4.18.