91Ó°ÊÓ

A ratio is a way to compare two quantities. It expresses how much of one thing there is relative to another.
For example, in our problem, we have two quantities: 102 and 100.
The ratio of these two numbers can be written as: \ \( \frac{102}{100} \) .
This notation shows that for every 100 units, there are 102 units. Ratios are often simplified to their smallest form but in this case, it is used as is to find the percent.
Ratios are useful in various aspects of mathematics and real-life problems because they provide a convenient way to compare and understand relationships between quantities.

A percent is a special way of expressing a ratio or a fraction in relation to 100.
The term 'percent' literally means 'per hundred'. When we say 'what percent', we mean 'what number out of 100'.
This is why our exercise asks '102 is what percent of 100?'. Using ratios, we can easily convert a number into its percent form.
In our problem, we set up the ratio \ \( \frac{102}{100} \) which means 102 out of 100. To denote this ratio as a percentage, we keep it as \ \( \frac{x}{100} \). Percentages are commonly used in daily life to represent discounts, statistics, and probabilities.

In many math problems, we often have to find an unknown value.
These unknowns are typically represented by variables such as \( x \). In our exercise, we are asked to find what percent 102 is of 100, where the percentage is our unknown value.
To find this unknown value, we set up an equation that represents the problem. We know 102 is our subject and 100 is the reference—so we let our unknown percent be \( x \).
The relationship is written as a proportion: \( \frac{102}{100} = \frac{x}{100} \) Using cross-multiplication or simple algebraic manipulation, we can solve for \( x \), which gives us the unknown percentage. Understanding how to set up and solve for unknown values is crucial for solving various mathematical problems.