A simple reverse engineering of calculation.

Question

I have a formula $x=\frac{1}{\frac{Y}{1000}}$ which is the calculation for converting Parallax to Parsec. I need to reverse it but can't remember how to reverse $1/$ .

So for a Parallax of $49.56$, divide by $1000$ then divide $1$ by $0.04956$ equals $20.17756$.

If I have $20.17756$, how do i get back to $49.56$ via $0.04956$.

I am looking for a simple explanation, one that can be calculated in a non-scientific calculator.

Thanks.

$Y/1000 = 1/x$. Can you finish? – Ethan Bolker Jan 13 '18 at 21:09 — Ethan Bolker, Jan 13 '18 at 21:09

score 0 · Accepted Answer · answered Jan 13 '18 at 21:11

0

Multiply both sides by $\frac{y}{1000}$: $$\frac{y}{1000}x=\frac{y}{1000}\cdot\frac{1}{\frac{y}{1000}}=\frac{\frac{y}{1000}}{\frac{y}{1000}}=1 $$ Now divide by $x$ (note that then $x\neq 0$): $$\frac{y}{1000}=\frac{y}{1000}\cdot\frac{x}{x}=\frac{\frac{y}{1000}x}{x}=\frac{1}{x}$$ Multiply by $1000$: $$y=1000\cdot \frac{y}{1000}=1000\cdot \frac{1}{x}=\frac{1000}{x}$$

answered Jan 13 '18 at 21:11

The Phenotype

5,199

So the answer is to divide 1 by 20.17756 then multiple 1000 – MiscellaneousUser Jan 13 '18 at 21:35
@MiscellaneousUser Yes, but this is equivalent to directly dividing 1000 by 20.17756, which is easier to do. – The Phenotype Jan 13 '18 at 21:40

A simple reverse engineering of calculation.

1 Answers1