Textbook Solution Accuracy: Are Rounded Calculations Affecting the Final Answer?

[QED-Kasper]

Homework Statement

Is the answer provided by the textbook solution manual wrong?
Here is the textbook exercise:

A bob with a mass of 0,500 kg is on the end of a long chord and suspended on a pivot (no friction). The distance of the center of mass of the the bob to the pivot-point is 250 cm. The bob is pulled 70 cm from its equilibrium state and then released.

a. Calculate the period.
b. Calculate the speed at which the bob passes its equilibrium state
c. How big is the Vibration energy?

Homework Equations

T=2$$\pi$$$$\sqrt{}(l/g)$$
V_max=2$$\pi$$A/T
E_vib=0,5mv²_max

The Attempt at a Solution

a. T=2$$\pi$$$$\sqrt{}(2,5/9,81)$$=3,17187=3,17 s
b. V_max=2$$\pi$$0,7/3,17187=1.386636=1,4 m/s
c. E_vib=0,5 x 0,5 x 1,386636²=0,48 J

for c. the textbook got 0,49 J

The textbook calculations are the same except that they use the rounded answers in each consecutive calculation. I thought that the correct way to calculate is to use the unrounded answers and then round the final answer to the correct significant figures. Am I right? Any help will be so much appreciated. (I'm sorry the equations aren't very pretty, it's my first time trying to use this system)

 

[GreatEscapist]

Well, we're doing this after spring break, so I guess I can't REALLY help.
But, my brother, dad, and aunt have a rant on physics- even though textbooks round every calculation YOU SHOULDN'T. In the end, two decimal places makes a huge difference. Even in high school physics homework. (I was 60 off one time because I put all of my calculations in sig figs)
So anyway, no- don't do that. And yes, books are wrong. Especially if you use Glencoe Physics.

 

[QED-Kasper]

Are you sure I'm doing it right? It happened to me a couple of times now, that I used unrounded answers in my calculations, which made my answer slightly different than the one in the textbook. Perhaps I'm using this rule in the wrong situations :s.

 

[Borek]

Never round down intermediate results.

If you report them - report them rounded down, as listing zillions of digits looks ugly and doesn't make much sense (they are mostly just noise), but if you are using them for further calcualtions - use them as you got them. If you have to copy them manually you don't need to copy everything, but using 2 or 3 guard digits is a must.

 

[QED-Kasper]

So my answers are correct, and the textbook is wrong?

 

[ash-kennard]

yes. you are definitely right.

 

[Phrak]

I agree. This rounding business hangs on from the long-dead age of sliderule calculations where anything over two digits was meaningless. It's been a bit over 30 years since calculators supplanted sliderules in general use in college courses, and it takes about one and one half generations for outmoded rules of thumb to die out...

 

[QED-Kasper]

ok thank you very very much guys :)