To find the formula for $z$ from the given equation $m = \left( \frac{z/f - g}{z/f} \right) \times 100$, follow these steps:

1. Start with the given equation: $m = \left( \frac{z/f - g}{z/f} \right) \times 100$

2. Simplify the fraction: $\frac{z/f - g}{z/f} = 1 - \frac{gf}{z}$ Hence, the equation becomes: $m = \left(1 - \frac{gf}{z} \right) \times 100$

3. Divide both sides by 100: $\frac{m}{100} = 1 - \frac{gf}{z}$

4. Isolate the fraction involving $z$: $\frac{gf}{z} = 1 - \frac{m}{100}$

5. Simplify the right-hand side: $\frac{gf}{z} = \frac{100 - m}{100}$

6. Invert both sides to solve for $z$: $\frac{z}{gf} = \frac{100}{100 - m}$

7. Finally, multiply both sides by $gf$: $z = gf \times \frac{100}{100 - m}$

Therefore, the formula for $z$ is: $z = \frac{100gf}{100 - m}$

Would you like any more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you derive a formula for $f$ given the other variables?
2. What happens to $z$ if $m$ approaches 100?
3. How does changing $g$ affect the value of $z$?
4. Can this formula be simplified further under certain conditions?
5. What is the physical meaning of each variable in a real-world context?
6. How does the relationship between $z$ and $m$ change if $f$ is very large?
7. Can you graph $z$ as a function of $m$ for fixed $g$ and $f$?
8. What if $m$ is negative? How does it affect $z$?

Tip: When manipulating equations, always perform operations symmetrically on both sides to maintain equality.