Death results from poor calculations. (1 Viewer)

[Uncle]

On February 25, 1991, during the Gulf War, an American Patriot Missile battery in Dharan, Saudi Arabia, failed to track and intercept an incoming Iraqi Scud missile. The Scud struck an American Army barracks, killing 28 soldiers and injuring around 100 other people.
It turns out that the cause was an inaccurate calculation of the time since boot due to computer arithmetic errors. Specifically, the time in tenths of second as measured by the system's internal clock was multiplied by 1/10 to produce the time in seconds. This calculation was performed using a 24 bit fixed point register.

24 bit timer stored 0.00011001100110011001100
Error = 0.0000000000000000000000011001100 . . . binary

Where in real numbers it is:

≈ 9.5 x 10⁻⁸

Timer running 100 hours : Error = 9.5 x 10⁻⁸× 100 × 60 × 60 × 10 = 0.342 seconds

The velocity of a SCUD missile is 1,676 m.s^-1

So the error is 1,676 m.s^-1 * 0.342 s = 573.192 m
Error > 0.5 km

Source:
UNSW MATH 2 0 8 9 Numerical Methods lecture slides.
The Patriot Missile Failure

An error resulting in a deviation of more than 500 metres is pretty huge, considering it is only a magnitude of 10⁻⁸.

The gist:

That's right, 28 people die from an error of 0.000000095

So,
Think twice before you just chop off numbers or just let one divided by square root of 3 equal just 0.5, when it is actually 0.5773502692...
Stop being lazy and just round off to only 1 decimal place or even one whole number when evaluating irrational expressions.

 

[Aquawhite]

I will NEVER round off again!

Lol, in exams I always write, by calc. Then I give it to decimal places ^_^

That is really interesting actually. Thanks for that UNCLE! <3

 

[Uncle]

Well, just be more careful in your rounding in your HSC exam.

If possible, give a rational expression in your third or second last line of working.

You may like to write your calculator display in your second last line of working,
then give an appropriately rounded answer in your last line, about 2 or 3 decimal places depending on the problem.

 

[Iruka]

Shouldn't round of until the end of the calculation. Of course, if you use a scientific calculator, it will be rounding off internally anyway.

 

[Studentleader]

Algebra is your friend - if a question doesn't ask for an exact answer never give one.

For example in chemistry titrations I'd use the calculator to solve:

C2 = 2(C1*V1)/V2

instead of

N1 = C1*V1
= some number
N2 = 2N1
= some number
C2 = N2/V2
= some number

On the subject on machine fail

* On September 21, 1997, a divide by zero error on board the USS Yorktown (CG-48) Remote Data Base Manager brought down all the machines on the network, causing the ship's propulsion system to fail.[2]