When x is small

[Edward Suarez 1I]

How small would x have to be to be ignored? (more so talking about when we "ignore x" when it is subtracted from a value when finding Kc for example) and how does this relate to the 5% initial to be a valid approximation?

[Harshita Talkad 4L]

x needs to be smaller than 10^(-3) to be ignored. This means it's small enough to be insignificant, which connects to the approximation being valid if it's within 5% because it means the x was small enough.

[Adrian C 1D]

Conceptually wise, its just seen that x is so insignificant compared to whatever it is being subtracted from. The example we used in class was that if you had one million dollars and you gave away one thousand dollars, you had essentially barely lost anything from the million dollars.

[Edward Suarez 1I]

x needs to be smaller than 10^(-3) to be ignored. This means it's small enough to be insignificant, which connects to the approximation being valid if it's within 5% because it means the x was small enough.

thank you!

follow up question: what happens if the approximation is not within 5%?

[Mukil_Pari_2I]

If the approximation is not within 5%, then the answer would not be valid. You would have to use the quadratic equation to figure out the value of x.