Hello all,

I've derived an equation in order to help model a physical system as part of a project I'm working on. I won't go into details as the part I need help with is only a small part of the project and really just involved simplify an equation. The equation as derived in its original form is:

Result = (V + Q - θY) - (1-θ)Y

Where θ is a coefficient that can vary between 0 and 1.

However I think this should simplify. For a start it can be re-written:

Result = V + Q - (θY + (1-θ)Y)

Then expanding out the (θY + (1-θ)Y) part gives θY + Y - θY, which equals just Y.

So bringing it all together I think the original equation should simplify:

Result = (V + Q - θY) - (1-θ)Y = V + Q - Y

Would it be possible for someone to check my maths and let me know if this is correct?

NOW - here comes the confusing bit. I programmed both the original equation and the simplifed equation into an Excel spreadsheet, then got the spreadsheet to generate random values for V, Q, Y and θ (with θ always between 0 and 1). The spreadsheet then compares the result from the original and simplifed equation. Theyshouldalways be equal (if I've done the simplification right) but every now and again Excel reports a difference in the results. It's always small, for instance:

1) Result 1a = 80.6000000000000, Result 1b = 80.5999999999999

2) Result 2a = 88.8554000000001, Result 2b = 88.8554000000000

i.e. very small differences. However I can never figure out why there is a difference. Have I done something wrong or is it just Excel reporting a difference which isn't actually there?

Thanks very much

-Rob