Quadratic Formula and Significant Figures

[spider-man]

QU 3. Find the smaller root of \(\displaystyle x^2\, +\, 0.4002x\, +\, 0.00008\, =\, 0\) using:
i) \(\displaystyle x\, =\, \dfrac{-b\, +\, \sqrt{b^2\, -\, 4ac}}{2a}\) and
ii) \(\displaystyle x'\, =\, \dfrac{-2c}{b\, +\, \sqrt{b^2\, -\, 4ac}}\),
rounding all numbers obtained at each step to 3 significant figures (NOT the same as 3 decimal places). Compare the results with the true solution \(\displaystyle x\, =\, -0.0002\).

I'm having trouble with the "3 sig fig" part.
a = 1
b = 0.4002
c = 0.0008

Do I have to initially express a,b,c in 3 sig figs? I'm not sure how.
Do I have to make my answer in 3 sig figs after every operation is computed? (square, add, subtract, divide)

 

[Bob Brown MSEE]

QU 3. Find the smaller root of \(\displaystyle x^2\, +\, 0.4002x\, +\, 0.00008\, =\, 0\) using:
i) \(\displaystyle x\, =\, \dfrac{-b\, +\, \sqrt{b^2\, -\, 4ac}}{2a}\) and
ii) \(\displaystyle x'\, =\, \dfrac{-2c}{b\, +\, \sqrt{b^2\, -\, 4ac}}\),
rounding all numbers obtained at each step to 3 significant figures (NOT the same as 3 decimal places). Compare the results with the true solution \(\displaystyle x\, =\, -0.0002\).

I'm having trouble with the "3 sig fig" part.
a = 1
b = 0.4002
c = 0.0008

Do I have to initially express a,b,c in 3 sig figs? (a,b,c) = (1, 0.400, 0.001)
Do I have to make my answer in 3 sig figs after every operation is computed? (square, add, subtract, divide) YES

http://en.wikipedia.org/wiki/Significant_figures#Identifying_significant_figures

Warning: These rules are NOT generally well accepted.
(a,b,c) = (1.00, 0.400, 0.000800) may be another interpretation.
You need to use the rules for sig figs provided by your teacher

BY THE WAY:
It is good that you asked,
"Do I have to make my answer in 3 sig figs after every operation is computed?"
The problem did ask you to do that (probably illustrating a point). You know that this is bad practice. Unless told (as you are here) carry full precision available and approximate at the end -- is the best practice,

 

[lookagain]

QU 3. Find the > > > smaller root < < <\(\displaystyle \ \ \ \ \ \) You are not looking for the smaller root. You are looking for the larger root.

of \(\displaystyle \ \ x^2\, +\, 0.4002x\, +\, 0.00008\, =\, 0\) using:


i) \(\displaystyle \ x\, =\, \dfrac{-b\, +\, \sqrt{b^2\, -\, 4ac}}{2a} \ \ \ \ \ \) <------ This gives the larger root. \(\displaystyle \ \ \ \)and


ii) \(\displaystyle \ x'\, =\, \dfrac{-2c}{b\, +\, \sqrt{b^2\, -\, 4ac}}\),


rounding all numbers obtained at each step to 3 significant figures (NOT the same as 3 decimal places).

Compare the results with the true solution \(\displaystyle \ x\, =\, -0.0002 \ \ \ \ \ \ \)<------- This is the larger root.

.

 

[spider-man]

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Ya, I asked my prof that before. He said he meant the absolute of the roots. I'm not sure why he meant that.