Significant Figures in Scientific Notation

[fonseh]

Homework Statement

I don't understand this question . The author want the at least 2 significant correct . why 0.5x10^(2-m) is used ?

It's not clear that the author want the answer to be less than 5 ?50? 0.5 ? 0.05 ?or 0.005?

Can someone explain it ?

Homework Equations

The Attempt at a Solution

 

[Buzz Bloom]

Hi fondeh:

I do not understand what you do not understand.

The author is describing the calculation of relative error between two successive estimates. The maximum for an acceptable relative error is given by the expression

0.5x10^(2-m), where m is the largest value that makes the expression larger than the a particular relative error.​

The the desired number of significant figures is 2. Therefore when the realtive error for an iteration produces m=2 to get the desired inequality, then that is the desired iteration.

Hope this helps some.

Regards,
Buzz

 

[fonseh]

Hi fondeh:

I do not understand what you do not understand.

The author is describing the calculation of relative error between two successive estimates. The maximum for an acceptable relative error is given by the expression

0.5x10^(2-m), where m is the largest value that makes the expression larger than the a particular relative error.​

The the desired number of significant figures is 2. Therefore when the realtive error for an iteration produces m=2 to get the desired inequality, then that is the desired iteration.

Hope this helps some.

Regards,
Buzz

since the largest significant figure is 2 , why shouldn't the 2-m = 2 , m = 0 ?

 

[fonseh]

given that 0.5x10^(2-m) , no matter it's 0.5 , 0.05 , 0.005 , it's still 1 significant right ?

 

[fonseh]

Hi fondeh:

I do not understand what you do not understand.

The author is describing the calculation of relative error between two successive estimates. The maximum for an acceptable relative error is given by the expression

0.5x10^(2-m), where m is the largest value that makes the expression larger than the a particular relative error.​

The the desired number of significant figures is 2. Therefore when the realtive error for an iteration produces m=2 to get the desired inequality, then that is the desired iteration.

Hope this helps some.

Regards,
Buzz

The 0.5x10^(2-m) is not given earlier in the question , it's given in the solution there ( author assume himself 0 ? why don't the author use fixed value ? e.g. 0.5 ? 0.05 ? or 0.005? .
why he use 0.5x10^(2-m) ?

 

[Mark44]

The question asks for the number of iterations for successive answers to agree in two decimal places. This means that the answers have to differ by less than 0.5 X 10^(-2), or .005.

 

[fonseh]

The question asks for the number of iterations for successive answers to agree in two decimal places. This means that the answers have to differ by less than 0.5 X 10^(-2), or .005.

0.5 X 10^(-2), or .005 is 3 decimal place , right ?

btw , the question ask for at least 2 significant figure , right ?? not decimal place ...

 

[Buzz Bloom]

btw , the question ask for at least 2 significant figure , right ?? not decimal place ...

given that 0.5x10^(2-m) , no matter it's 0.5 , 0.05 , 0.005 , it's still 1 significant right ?

since the largest significant figure is 2 , why shouldn't the 2-m = 2 , m = 0 ?

Hi Fonesh:
You are right. 2 significant figures , not decimal places.

Regarding "0.5 , 0.05 , 0.005 , it's still 1 significant", what is desired is the iteration which first shows 2 significant figures. The number of significant figures in the value of the expression 0.5x10^(2-m) is not relevant.

The author's intention is to teach you about the expression 0.5x10^(2-m) as a way to determine the number of significant figures in an iteration. Since 2 figures are wanted, m=2 when the desired iteration satisfies the inequality about the relative change between two consecutive iterations. That means that the iteration for which m= 2 (or 0.5x10^(2-m)=0.5%), which means the relative difference < 0.5%, is the desired iteration.

I think the way the author presented this without any discussion to explain it is unfortunate. It would perhaps have been clearer if the author had written, "0.5x10^(2-m)%".

Regards,
Buzz

 

[Mark44]

Regarding "0.5 , 0.05 , 0.005 , it's still 1 significant", what is desired is the iteration which first shows 2 significant figures. The number of significant figures in the value of the expression 0.5x10^(2-m) is not relevant.

I agree. In my earlier post I was thinking in terms of two decimal places, not two significant digits.