What are the uncertainty values for my corrected magnitudes?

[Thomas Smith]

Homework Statement

I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations

Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
$\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}$[/B]

The Attempt at a Solution

Error in Corrected g band $\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}$ = 0.033030

Error in Corrected r band $\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}$ = 0.022850[/B]

 

[Thomas Smith]

Homework Statement

I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations

Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
$\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}$[/B]

The Attempt at a Solution

Error in Corrected g band $\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}$ = 0.033030

Error in Corrected r band $\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}$ = 0.022850[/B]

I'm unsure about the brackets in the equation. Is this correct? $\sqrt{((a/b)^2 + (x/y)^2)}$
Or should it be $\sqrt{(a/b)^2 + (x/y)^2}$

 

[haruspex]

I'm unsure about the brackets in the equation. Is this correct? $\sqrt{((a/b)^2 + (x/y)^2)}$
Or should it be $\sqrt{(a/b)^2 + (x/y)^2}$

I don't see a functional difference.