What Went Wrong with My Calculation on Significant Figures?

[tfsc]

I'm currently re-teaching my self maths to get into physics as i sucked at maths in school but now I am older I feel like actually learning it !

So I'm on a website which gave me a test quiz i got them all correct bar one but it won't tell me the answer so ill show you the question and my answer see if you can help work out where i have miscalculated.Solve the following problem with correct numbers of significant digits:
2.1 * 5.2 - 1.45 / 0.02303

My workings:

1.45 / 0.2303 = 6.296135475466782457663916630482
2.1 * 5.2 = 10.92

10.92 - 6.296135475466782457663916630482 = 4.623864524533217542336083369518

Rounded to lowest significant digits in the sum.
So my answer was: 4.6

But that's incorrect.

Any ideas where i went wrong in my steps?

 

[chiro]

Hey tfsc and welcome to the forums.

Take a look at this line:

1.45 / 0.2303

Is there a missing 0? ;)

 

[tfsc]

Well i thought this at first but according to the documentation of what classifies as a significant digit it says:

The significant digits represent the valid digits of a number. The following rules summarize the significant digits:

Nonzero digits are always significant.
All final zeros after the decimal points are significant.
Zeros between two other significant digits are always significant.
Zeros used solely for spacing the decimal point are not significant.

So that one 0 is not significant so you don't calculate with it. =/Argh i figured it out now - the rules regarding rounding up and down were little confusing ! Also it appears you do include the insignificant numbers during calculation so the answer is -52.

 

[chiro]

When you are dealing with significant figures or rounded answers, you can't change the numbers involved in the calculation. The thing that you have to process is the final answer and not any of the existing data that you are given.

 

[HallsofIvy]

Saying that a zero, used for placement of the decimal point, is not significant does not mean you can simply ignore it. 0.0203 is simply not the same number as .203 whether you are thinking "significant" figures or not. To really work with significant figures, use scientific notation: to two significant figures, 0.02303 is $2.3 \times 10^{-2}$.


chiro's statement that you should not round until the end is not entirely true- though it is a good idea to include at least one more significant figure in each calculation than you want at the end. To three significant figures, 0.02303 is $2.30\times 10^{-2}$, so 1.45/0.02303 becomes $\frac{1.45}{2.30}\times 10^2= 0.630 \times 10^2= 6.30\times 10^1= 63.0$.