Problem 79 - Algebra 1: Concepts and Skills

Question

Write the given fraction, decimal, or percent in the indicated form. Write \(\frac{53}{25}\) as a percent.

Step-by-Step Solution

Answer

The fraction \(\frac{53}{25}\) in percentage form is 212%.

Step 1: Converting Fraction To Decimal

To convert a fraction to a decimal, divide the numerator by the denominator. Thus, \( \frac{53}{25} \) in decimal form is \(\frac{53}{25} = 2.12\).

Step 2: Converting Decimal To Percent

To convert a decimal into percent, multiply it by 100. Hence, 2.12 in percentage is \(2.12 * 100 = 212\%\).

Key Concepts

Decimal to Percent Conversion

Converting decimals to percents is an essential math skill that allows us to express numbers in a way that can be more intuitive, especially when dealing with portions or comparisons. The process is straightforward: you simply multiply the decimal number by 100 and add a percent sign to the result. This transforms the value into a percentage, which reflects how many parts out of a hundred the original decimal represents.

For instance, let's take the decimal 0.75. When converted into a percentage, it becomes:
\( 0.75 \times 100 = 75\% \).
It's easy to understand that 0.75 of something is the same as 75 out of 100 parts—essentially, 75%.

Fraction to Decimal Conversion

Understanding how to convert fractions to decimals is a necessary step in various mathematical calculations, including those related to percents. A fraction represents a part of a whole and consists of two numbers: the numerator (top number) and the denominator (bottom number). To convert a fraction to a decimal, you divide the numerator by the denominator.

For example, to convert the fraction \( \frac{3}{4} \) to decimal, perform the division 3 ÷ 4, which equals 0.75. It's important to note that some fractions will result in a repeating decimal, which can often be rounded to simplify the number for practical use.

Understanding Percents

Percents are a way of expressing ratios as parts of 100. The term 'percent' literally means 'per hundred', which is symbolized by the '%' sign. In daily life, percents are used to communicate discounts, interest rates, statistics, and much more. They provide a straightforward way to compare numbers and understand portions on a common scale.

It's crucial for students to grasp that percents, decimals, and fractions are just different ways of expressing the same thing. For instance, 50% can also be written as 0.5 or \( \frac{1}{2} \). Each form has its own use, with percents usually being the preferred form when talking about rates or proportions in everyday contexts. Understanding percents involves recognizing that a percent less than 100% denotes a part smaller than the whole, while a percent greater than 100% indicates a part larger than the whole, which can happen in cases of growth or increase.