Problem 54 - Prealgebra

Question

Write \(\frac{1}{200}\) as a percent.

Step-by-Step Solution

Answer

0.5%

Step 1: Understanding Percent Conversion

To convert a fraction to a percent, you need to express it as a fraction with a denominator of 100 because 'percent' means 'per one hundred'. This involves multiplying the fraction by 100%.

Step 2: Applying the Conversion

Start with the fraction \( \frac{1}{200} \). To convert this to a percent, multiply by 100%: \[ \frac{1}{200} \times 100\% \]

Step 3: Calculating the Result

Perform the multiplication: \[ \frac{1 \times 100}{200} = \frac{100}{200} \].

Step 4: Simplifying the Fraction

Now, simplify the fraction \( \frac{100}{200} \) by finding the greatest common divisor of 100 and 200, which is 100. \[ \frac{100 \div 100}{200 \div 100} = \frac{1}{2} \].

Step 5: Converting to Decimal

Now, convert the simplified fraction to a decimal. \( \frac{1}{2} = 0.5 \).

Step 6: Expressing as a Percent

Since we are converting \(0.5\) into a percent, you multiply by 100 to get \(0.5 \times 100 = 50\%\). Thus, \(\frac{1}{200}\) is equivalent to 0.5%.

Key Concepts

Fraction to Percent

Converting a fraction to a percent is essential for many real-life applications. It helps compare numbers on a common scale, making it easier to understand their magnitude relative to a whole. The term 'percent' essentially means 'per hundred', which suggests that any number expressed as a fraction of 100 is a percentage.

To convert any fraction into a percent, follow these steps:

• Multiply the fraction by 100, as percentages are based on a denominator of 100.
• Add the percent symbol (%) to indicate it as a percentage.

By understanding this simple concept, you can quickly convert fractions to percentages and vice versa. It simplifies comparing different values and aids in better interpretations of statistical data.

Simplifying Fractions

Simplifying fractions means reducing them to their simplest form, making calculations easier. A fraction is considered simplified when its numerator and denominator are as small as possible while still being whole numbers. This is achieved by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Here's what you should do:

• Find the greatest common divisor of the numerator and the denominator.
• Divide both the numerator and the denominator by the GCD.

For example, to simplify the fraction \( \frac{100}{200} \), notice that both numbers can be divided by 100, their greatest common divisor. Thus, it simplifies to \( \frac{1}{2} \). This type of simplification is a foundational skill in mathematics that aids in easier problem-solving and clearer communication of results.

Decimal Conversion

Converting fractions to decimals is another practical skill in math that simplifies understanding and computation. A decimal is a special form of a fraction whose denominator is a power of 10, thus making it easier to use in calculations.

To convert a fraction to a decimal:

• Divide the numerator by the denominator.
• Round the result to the desired number of decimal places, if necessary.

Using the fraction \( \frac{1}{2} \), dividing 1 by 2 results in 0.5. This process translates fractions from their conventional form into a decimal form, which is often more convenient for visualizing sizes and performing calculations in various fields.

Mathematical Calculation Steps

Mathematical calculation steps are essential for clear and concise problem-solving, enabling systematic approaches to finding solutions. Breaking down problems into smaller, manageable parts leads to stronger comprehension and accurate results.

Here’s a general approach to follow:

• Identify the problem and what you need to find.
• Write down all known values and relationships.
• Apply relevant mathematical operations to progress step-by-step toward a solution.
• Recheck each step for accuracy and correct logic.

For example, converting \( \frac{1}{200} \) to a percent requires sequential steps: multiply by 100 to shift the fraction to a percentage base, simplify the ensuing fraction, and convert any results into decimals if needed for clarity. Page by page, preview the solution before finalizing for consistency and completion.