Problem 26 - Prealgebra

Question

Change to percent. $$\frac{200}{2,400}$$

Step-by-Step Solution

Answer

The percent form of \(\frac{200}{2,400}\) is 8.33%.

Step 1: Understand the Meaning

To express a fraction as a percent, you essentially want to know how many parts out of 100 the fraction represents. Percentages are simply fractions with a denominator of 100.

Step 2: Divide the Fraction

Start by dividing the numerator of the fraction by the denominator. This will give you a decimal. Perform the division \(\frac{200}{2,400}\): \[\frac{200}{2,400} = 0.0833\dots\]

Step 3: Convert the Decimal to a Percent

To convert the decimal obtained from dividing into a percentage, multiply it by 100. Thus, \[0.0833 \times 100 = 8.33\%\]

Step 4: Round if Necessary

If rounding is required or more appropriate, decide on the level of precision. In many cases, rounding to one or two decimal places suffices. Here, 8.33% is sufficiently precise without further rounding.

Key Concepts

Converting Fractions to Decimals

To convert a fraction into a decimal, you need to perform a simple division operation. Every fraction consists of a numerator and a denominator. In mathematical terms, the fraction represents the division of the numerator by the denominator. For instance, in the fraction \( \frac{200}{2,400} \), you divide 200 by 2,400. Performing the division gives you the decimal: \[\frac{200}{2,400} = 0.0833\dots \]Here’s a simple process to follow:

• Write down the fraction.
• Divide the numerator by the denominator using a calculator or long division.
• The result is your decimal form.

Always remember, converting fractions to decimals may sometimes result in repeating decimals. However, you can round them to an appropriate number of decimal places for simplicity.

Converting Decimals to Percents

Once you have a decimal, converting it to a percent is straightforward. A percent is simply the decimal multiplied by 100. This conversion reflects how many parts the decimal represents per hundred.For example, if you have 0.0833, you convert it to a percent by multiplying as follows:\[0.0833 \times 100 = 8.33\%\]It’s helpful to remember:

• Move the decimal point two places to the right to effectively multiply by 100.
• Add the percent symbol (%) to indicate the conversion.

Understanding decimal to percent conversion is crucial, as many real-world applications require expressing numbers in percent format for clarity.

Simplifying Fractions

Simplifying fractions entails reducing them to their smallest possible form, where the numerator and denominator have no common factors other than 1. This can make calculations more straightforward and results more understandable.To simplify \( \frac{200}{2,400} \), identify the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD is 200. Divide both by this number:\[\frac{200 \div 200}{2,400 \div 200} = \frac{1}{12} \]Steps to simplify fractions include:

• Determine the GCD of the numerator and denominator.
• Divide both numerator and denominator by the GCD.
• Write the simplified fraction.

A fraction in its simplest form is often easier to work with and can lead to more intuitive understanding and communication of mathematical concepts.