Problem 48 - Algebra 1: Concepts and Skills

Question

Write the percent as a decimal. \(25 \%\)

Step-by-Step Solution

Answer

The decimal equivalent of \(25\%\) is \(0.25\).

Step 1: Identify the Percentage

The given percentage is \(25\%\).

Step 2: Convert Percent to Decimal

To convert the percentage to a decimal, divide the given percentage by \(100\). Alternatively, you can simply move the decimal point two places to the left. This gives us \(0.25\).

Key Concepts

Percentage

A percentage is a way to express a number as a fraction of 100. It is denoted by the symbol "\(\%\)". Understanding percentages is crucial for financial literacy, data interpretation, and even everyday decisions like shopping discounts.

• When you see a percentage, think of it as a part of a whole that is divided into 100 equal parts. For instance, \(25\%\) means 25 out of 100 parts.
• Percentages can easily be converted to other forms, such as decimals and fractions, to facilitate easier calculations and comparisons.

To get comfortable with percentages, practice converting them into decimals and fractions regularly. This will improve your ability to quickly and accurately interpret and work with percentages in various contexts.

Decimal Notation

Decimal notation is a standard system for representing numbers using the base 10 system. Decimals are used to show values that are less than one or more than one, without the use of fractions.
When converting a percentage like \(25\%\) to decimal notation, you need to understand a couple of principles:

• Dividing by 100: This is because percentages are fundamentally out of 100. By dividing by 100, you align the percentage with its base numeric value in decimal form. Hence, \(25\%\) becomes \(0.25\).
• Moving the Decimal: Alternatively, just move the decimal point two places to the left, which is a quick method. So \(25.0\%\) naturally shifts to become \(0.25\).

Understanding and using decimal notation is essential in many fields such as mathematics, science, engineering, and finance, as it provides a clear and concise representation of numbers.

Basic Arithmetic

Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division. These operations form the foundation of all mathematical calculations and are crucial in converting percentages to decimals.
In the example of converting \(25\%\) to a decimal:

• Division is the key operation. By dividing \(25\) by \(100\), you actually perform a simple arithmetic operation to achieve \(0.25\).
• Understanding this operation facilitates various calculations involving percentage reductions, interest rates, and proportions.

Being adept at basic arithmetic not only simplifies conversions but also enhances problem-solving skills needed in daily life and academic settings. It's always handy to practice these operations to maintain accuracy and speed in calculations.