Question

If Q = `"X"^"n"/"Y"^"m"` and Δx is absolute error in the measurement of X, Δy is absolute error in the measurement of Y, then absolute error ΔQ in Q is ______.

Options

• ΔQ = `+- ("n" (Delta x)/x + "m"(Delta "y")/"y")`

• ΔQ = `+- ("n" (Delta x)/x + "m"(Delta "y")/"y")"Q"`

• ΔQ = `+- ("n" (Delta x)/x - "m"(Delta "y")/"y")"Q"`

• ΔQ = `+- (("n" Delta x)/x - ("m"Delta "y")/"y")`Q

Answer 1

If Q = `"X"^"n"/"Y"^"m"` and Δx is absolute error in the measurement of X, Δy is absolute error in the measurement of Y, then absolute error ΔQ in Q is `underline(Δ"Q" = +- ("n" (Delta x)/x + "m"(Delta "y")/"y")"Q")`.

Explanation:

Here, maximum fraction error is:

`(Δ"Q")/"Q" = +- ("n" (Δ x)/x + ("m" Δ"y")/"y")`

∴ Absolute error in Q, i.e.,

ΔQ = `+- ("n"(Delta x)/x + ("m"Delta"y")/"y")`Q