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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.

The Phenotype
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1 Answers1

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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 $1000$: $$y=1000\cdot \frac{y}{1000}=1000\cdot \frac{1}{x}=\frac{1000}{x}$$

The Phenotype
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