For the given proportion, find the unknown number $n$.
$\frac{n}{0.9}=\frac{0.01}{10}$
$n =$ □ (Type an integer or a decimal)
We are given the following proportion equation involving the unknown variable \(n\):
\[\frac{n}{0.9} = \frac{0.01}{10}\]
Our objective is to solve for the value of \(n\). This is a standard algebraic problem where we can isolate \(n\) using the properties of proportions. We know that for any proportion of the form \(\frac{a}{b} = \frac{c}{d}\), the cross-multiplication property holds, which states that \(a \times d = b \times c\).
Applying the cross-multiplication property to our equation, we multiply the numerator of the left side by the denominator of the right side and vice versa:
\[n \times 10 = 0.9 \times 0.01\]
Next, we calculate the product on the right side:
\[0.9 \times 0.01 = 0.009\]
So the equation simplifies to:
\[10n = 0.009\]
To solve for \(n\), we divide both sides of the equation by \(10\):
\[n = \frac{0.009}{10}\]
Dividing a decimal by 10 shifts the decimal point one position to the left:
\[n = 0.0009\]
Thus, the value of the unknown number is \(0.0009\).
Proportions are fundamental in many real-life applications, such as adjusting a recipe, calculating map distances, or determining the concentration of a chemical solution. For instance, if a laboratory protocol specifies that 0.9 ml of a reagent must be used for every 10 ml of a solution, and you need to determine the amount \(n\) of the reagent needed for a specific trial where the ratio must be kept constant relative to a 0.01 concentration baseline, you would use this exact algebraic method. Mastering proportions allows you to scale values precisely and maintain consistency in scientific and everyday tasks.