Methods of Approximation Problem (1 Viewer)

[slip]

Does anybody know how to be sure your answer is correct to n decimal places.

for example if the quesiton says find a root of f(x) correct to 2 decimal places (when do you know that your correct to 2 decimal places)

 

[ToO LaZy ^*]

when you have 2 numbers after the decimal, but don't forget to round up/round down.

 

[slip]

sorry this is confusing i dont mean rounding.

like say that want you to approximate x^3 - 2 = 0

the correct answer is like 1.42 or whatever. and they want the answer correct to 2dp.

but your first approximation is 1.53 or whatever. when will you know you have the correct answer to 2 dp with out solving the original equation precisely with another method.

 

[CrashOveride]

They will usually say "using Newton's method twice" etc. So you know how many times to do it.

 

[mojako]

Halving the interval: Each successive application will halve the uncertainty. Final solution would be a < x < b, where a should be rounded down and b rounded up. For example, 1.436... < x < 1.444... becomes 1.43 < x < 1.45, then x = 1.4 since the last decimal place is not accurate (they're different).
Newton's method: The number of correct decimal places generally doubles with each application. Similar to halving the interval, if you get x_1 = 1.436 and x_2 = 1.444 then it's only accurate to the first decimal place.
If when you try to find x_3 you get x_3 = 1.449, your answer now is 1.44 correct to the second decimal place, for most equations anyway.

 

[slip]

hey yeh i think that is what i need to know. thank you everybody.