Problem 72 - Elementary Algebra

Question

Convert to a decimal. \(538 \%\)

Step-by-Step Solution

Answer

The decimal equivalent of 538% is 5.38.

Step 1: Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. In this case, 538% represents 538 out of 100.

Step 2: Converting Percentage to Decimal

To convert a percentage to a decimal, you divide the percentage by 100. Since we want to convert 538% to a decimal, we divide 538 by 100.

Step 3: Calculation

Perform the division: \[ 538 \div 100 = 5.38 \] So, the decimal equivalent of 538% is 5.38.

Step 4: Verification

To ensure the conversion is correct, multiply 5.38 by 100 to see if you revert to the original percentage: \[ 5.38 \times 100 = 538 \] This confirms that 5.38 is indeed the correct decimal form of 538%.

Key Concepts

Understanding Percentage Calculations

Percentage calculations are common in math, helping translate points of data into a meaningful comparison. A percentage itself is simply a part of 100. It's used to show how large or small a number is compared to a base figure, usually 100. When you see something like 538%, think of it as 538 portions of 100. The % sign is a shorthand that saves us from constantly writing out fractions.

• "Percent" comes from the Latin "per centum" meaning "by the hundred."
• Common uses include calculating discounts, interest rates, and statistics.
• Always ensure clarity by converting percentages to more straightforward numbers for calculations.

Understanding the fundamentals can help remove confusion when dealing with larger or smaller percentages, making mathematical operations easier to handle.

Decimal Conversion Explained

Decimal conversion is the process of turning a percentage into a decimal, making it easier to use in calculations. Converting percentages to decimals is a vital step in many mathematical and real-world applications. The main idea is to divide by 100 because percentages describe how much out of a 100. Here's how to do it:

• Take the percentage number. For example, 538.
• Remove the percentage symbol (%).
• Divide the number by 100 as part of decimal conversion. Doing so shifts the decimal point two places to the left, turning 538% into 5.38.

By putting it in decimal form, you simplify subsequent operations and get an accurate representation that can interact smoothly with other numbers.

Importance of Mathematical Operations

Mathematical operations play a crucial role in manipulating percentages and decimals to suit your needs. After converting a percentage to a decimal, mathematical operations like addition, subtraction, multiplication, or division are much easier.

• The conversion to decimal is verified by reversing the process, confirming accuracy.
• With decimals, calculations become uniform and straightforward.
• Validate your conversions by multiplying the decimal by 100; you should get the original percentage.

Simplifying calculations through conversion allows you to handle complex and large-scale data without hassle. This process ensures precision, especially when working with financial data, growth rates, or statistical analysis.