Problem 34 - Elementary Algebra

Question

Convert each percent to its decimal equivalent. $$ 25 \% $$

Step-by-Step Solution

Answer

25% as a decimal is 0.25.

Step 1: Understanding Percent

A percent represents a part out of 100. So, if you have 25%, it means 25 out of 100 or 25/100.

Step 2: Convert Percent to Decimal

To convert a percentage to a decimal, you divide by 100. This step changes 25% into a decimal by calculating: \( \frac{25}{100} \).

Step 3: Simplifying the Fraction

Calculate the division \( \frac{25}{100} \), which equals 0.25.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of a whole, using 100 as the reference point. When you see a percentage, think of it as a fraction that has 100 as the denominator. For instance, saying 25% is like saying 25 out of 100. This is why percentages are so useful—because they make it easy to compare different quantities on the same scale.
Imagine looking at a pie chart where the entire pie represents 100%. Each slice corresponds to a particular percentage of the pie. So, if you eat a slice that's 25% of the pie, you've consumed 25% of the whole pie.

• Percent means "per hundred"
• Expressed using the symbol %
• Helps in comparing proportions

Fractions

Fractions describe a portion of a whole in terms of two numbers: a numerator and a denominator. The numerator indicates how many parts you have, while the denominator shows the total number of equal parts there's been divided into.
In the context of percentages, a percent can straightforwardly be converted into a fraction by considering the percentage as the numerator and 100 as the denominator. For example, 25% becomes \( \frac{25}{100} \). This fraction representation is fundamental for converting percentages into decimals, which is a key skill in many math-related tasks.
Fractions are versatile and are used to perform calculations in elementary and advanced mathematics. They are essential in understanding decimal conversion and are pivotal in mathematical problem-solving.

• Composed of numerator and denominator
• Percent expressed as a fraction: 25% = \( \frac{25}{100} \)
• Useful in calculations and conversions

Decimal Representation

Decimal representation is a standard way of expressing numbers using the base ten. When converting percentages to decimals, the key process involves dividing the percentage number by 100. This division shifts the decimal point two places to the left, transforming the percentage into its decimal form.
From our example, 25% as a percentage becomes 0.25 when converted to a decimal. This method of representation is efficient for calculations in various fields—such as finance and data analysis—due to its ease of handling compared to fractions. Once mastered, converting between percentages, fractions, and decimals becomes a seamless task.

• Base-10 number system
• Converting percent to decimal: 25% = 0.25
• Simplifies mathematical computations