How to Solve for a Number Given a Percentage: Step-by-Step Guide

Understanding how to solve for an unknown number using percentages is a valuable skill in math. Let's break down the process step-by-step using the example: '9 is 0.03 of what number?'

First, recognize that the phrase 'is 0.03 of' indicates a multiplication relationship. This means that 0.03 times some unknown number, which we will call 'x', equals 9. Therefore, we can write the equation:

$$9 = 0.03 * x$$.

To make this easier to work with, we convert the decimal 0.03 into a fraction. Remember that 0.03 is the same as 3 hundredths, which can be expressed as the fraction:

$$\frac{3}{100}$$.

Now, we can rewrite our equation using this fraction:

$$9 = \frac{3}{100} * x$$.

To isolate x, we need to get rid of the fraction on the right side. This can be done by dividing both sides of the equation by $$\frac{3}{100}$$. However, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $$\frac{3}{100}$$ is $$\frac{100}{3}$$. Therefore, we multiply both sides by $$\frac{100}{3}$$:

$$x = 9 * \frac{100}{3}$$.

Calculating this gives:

$$x = 9 * \frac{100}{3} = \frac{900}{3} = 300$$.

Thus, the unknown number is 300!

This method can be applied in various real-world situations, such as calculating discounts, determining percentages in statistics, or even in financial contexts where understanding fractions and percentages is crucial. For instance, if you wanted to find out how much a discounted item costs when you know the discount percentage and the sale price, this approach would be very useful.

In summary, by turning a percentage into a fraction, you can easily set up an equation to find unknown values. This skill not only enhances your mathematical abilities but also prepares you for practical applications in everyday life. Remember to practice with different numbers and percentages to strengthen your understanding!