Solve 9/120=a/10^n

$$\frac { 9 } { 120 } = \frac { a } { 10 ^ { n } }$$

Solve for a

$$a=\frac{3\times 10^{n}}{40}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{9}{120} to lowest terms by extracting and canceling out 3.

$$\frac{3}{40}=\frac{a}{10^{n}}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{a}{10^{n}}=\frac{3}{40}$$

The equation is in standard form.

$$\frac{1}{10^{n}}a=\frac{3}{40}$$

Divide both sides by 10^{-n}.

$$\frac{\frac{1}{10^{n}}a\times 10^{n}}{1}=\frac{\frac{3}{40}\times 10^{n}}{1}$$

Dividing by 10^{-n} undoes the multiplication by 10^{-n}.

$$a=\frac{\frac{3}{40}\times 10^{n}}{1}$$

Divide \frac{3}{40} by 10^{-n}.

$$a=\frac{3\times 10^{n}}{40}$$

Solve for n

$$n=\log(e)\left(\ln(a)+\ln(\frac{40}{3})\right)$$

$$a>0$$