How do you know how many significant figures to give your answer to?

If the question doesn't state how many, how do you know what to round it too as i've lost marks on papers by not doing it to the correct number of s.fs. for example if the question was: how many moles of a solution with a concentration of 4.123 moldm-1 and a volume of 6.32 dm3? If you multiplied them, you'd get 26.05736 moles, but what would you round to?

Reply 1

s.xw

3 s.f. because that's the lowest number of s.f. given in the question. For my A levels, this is not stated at the front of the exam paper, but teachers stress it.

Reply 2

Bertybassett

Original post by s.xw

3 s.f. because that's the lowest number of s.f. given in the question. For my A levels, this is not stated at the front of the exam paper, but teachers stress it.

so you always round to the least number of sig figs given in the question for the numbers involved?

Reply 3

s.xw

Original post by Bertybassett

so you always round to the least number of sig figs given in the question for the numbers involved?

Unless otherwise stated. It's not as common in maths, but common in physics and chemistry (be careful though because sometimes the given RAM is meant to be taken as accurate).

But definitely do this when they state round to an appropriate number of digits. Marks schemes usually give you some leeway in other questions. In A-level physics for example, saying 2.131342 seconds is pretty much meaningless. Just check that your rounding makes sense.

(edited 6 years ago)

Reply 4

Fonzworth

3 sf is the highest you should do. Normally you do it to the smallest number you’re given

e.g. 5.25282 + 7.3 = 2 sf because that’s the smallest they’ve done it

Reply 5

Student-95

Original post by Fonzworth

3 sf is the highest you should do. Normally you do it to the smallest number you’re given

e.g. 5.25282 + 7.3 = 2 sf because that’s the smallest they’ve done it

This is false. For multiplication/division you use the lowest number of significant figures but for addition/subtraction you should go to the lowest number of decimal places instead.

Reply 6

Bertybassett

Original post by Student-95

This is false. For multiplication/division you use the lowest number of significant figures but for addition/subtraction you should go to the lowest number of decimal places instead.

im confused now

Reply 7

Student-95

Original post by Bertybassett

im confused now

It's to do with error proogation - the number of significant figures/decimal places isn't arbitrary there's logic behind it. Just Google it and you should be able to find a more detailed explanation.

This source covers the basics: http://chemistry.bd.psu.edu/jircitano/sigfigs.html

(edited 6 years ago)

Reply 8

Fonzworth

Original post by Bertybassett

im confused now

7.637392728 x 4.3 = 2 sf as that’s the lowest

26.89 + 3.25180 = full number + 2 decimal places as that’s the lowest

Is that right @Student-95?

Reply 9

Student-95

Original post by Fonzworth

7.637392728 x 4.3 = 2 sf as that’s the lowest

26.89 + 3.25180 = full number + 2 decimal places as that’s the lowest

Is that right @Student-95?

33 for the multiplication (2sf)
30.14 for the addition (2dp)

Reply 10

Bertybassett

Original post by Student-95

33 for the multiplication (2sf)
30.14 for the addition (2dp)

how do you know?

Reply 11

Student-95

Original post by Bertybassett

how do you know?

Know what? You can check the full value on a calculator and the rounding is based on the rules I mentioned above.

Reply 12

tahmidbro

What if i calcuate relative atomic mass of an element using m/e values and relative abundances? This operation requires both multiplication and addition. How to round up the value of relative atomic mass in this case?