The discussion revolves around justifying the number of significant figures for a variable 'x' derived from an equation, specifically in the context of an experiment measuring the mass of a mug. Participants are exploring the implications of significant figures in calculations involving measured values and constants.
The discussion is active, with participants seeking clarification on the rules governing significant figures. Some have offered guidance on how to approach the justification of significant figures based on the values involved, while others express confusion about specific examples and the nature of constants.
Participants are navigating the complexities of significant figures, particularly in relation to constants and measured values. There is an ongoing exploration of whether certain values can be considered exact known numbers and how this affects the final significant figures in calculations.
Yes, I think that is the example of what i said.. Please show the equation that you used to solve for x. You said that x had 3 sig figures...does it?? You can only justify as many sig figures in your answer as sig fig rules allow. If y = zx, then x =y/z, and if y is 2.42 and z is 1.23, then the answer for x is 1.97, not 1.96747967..., because there are only 3 sig figures in the values of y and z, and therefore x can only have 3 sig figures, not a whole bunch of them. Am I understanding your question correctly?koat said:thanks but that's not actually what i mean with my x- value.
the x value was an unknown in an equation and i had to work out this x value.
it represents the mass of a mug.
then after i have made the x value the subject of my equation they ask me that question which i have written in my first post.
what do i have to do?
and what does justify mean in this context?
Then the answer should have 3 significant figures.koat said:but in my equation the 0.6 is an exact known number and all the other numbers are measured to3 sf
how about now?
PhanthomJay said:Then the answer should have 3 significant figures.
Yes, if the 0.6 is an exact known number, it theoretically has an infinite number of significant digits, that is, you can call it 0.6000000000000000000. In multiplying or dividing, the result can have only as many significant figures as the least number of significant values in any number used in the problem, so that in your case, x must have 3 significant figures. As an example, if y = 1.23 (3 sig figures) and z = 0.629 (3 significant figures), then x = y/0.6z = 1.23/0.6(.629) = 3.26 (3 sig figs). The real difficulty is in determing the number of sig figs in a number, for sample, if experimentaly, one value is 0.002 (1 significant figure) and the other value is 0.111 (3 sig figures), and you wanted to multiply them together, then the answer is (.002)(.111) = 0.0002 (which has 1 sig fig), not 0.000222, which would have 3 sig figs, which is too many to use. Confusing.koat said:sorry to ask again but is it right what I have understood so far.
When I 've got y=0.6zx then you get x=y/0.6z
At school we measured y and z to 3 sf. So does it mean that 0.6 is kind of a constant value and it doesn't affect the value of x which I am trying to work out? Because I didn't work out 0.6. This was the only number given in the equation but the other numbers which I have plugged into the equation are measured values.
So does x also have 3 sf then?
Can you explain that again please. I am slightly confused.
Thanks in advance
Yes, correct, as long as the constant that is given to you is an exact known number. Sometimes the number 'pi' is given to you as 3.14 even though its value is 3.14159... .koat said:When you say 0.6 is an exact known number is that the same as saying it's a constant?
And are you trying to tell me that a constant doesn't affect the final result ?
Am i right?
If I would have this example:
(0.333)(0.550)/0.2
where 0.2 is the value already given in the equation( so a constant?) and 0.333 and 0.550 are measured values. Is the answer going to have 3 sf?
yes, the ans has 3 sig figskoat said:Ok I understand what you are saying but can you also answer the last bit of my question with the calculation please :)
it has 3. The number 0.005 has 1. Google on 'significant figures'.And does 0.550 actually have 2 or 3 sf?
You don't know for sure unless you can identify it as such or were given it as such. For example, the area of a right triangle is 0.5(b)(h). The 0.5 is exact in this example.And how do I know that 0.2 is an exact known number- this value is just given in the equation ?
thanks