Problem 79 - Prealgebra

Question

Use a calculator to write each fraction as a decimal, and then change the decimal to a percent. Round all answers to the nearest tenth of a percent. $$\frac{236}{327}$$

Step-by-Step Solution

Answer

72.2%

Step 1: Convert Fraction to Decimal

First, divide the numerator (236) by the denominator (327) to convert the fraction to a decimal. Use your calculator to perform the division: \[ \frac{236}{327} \approx 0.7217 \]

Step 2: Convert Decimal to Percentage

To convert the decimal to a percentage, multiply the decimal value by 100. 0.7217 multiplied by 100 equals 72.17.

Step 3: Round the Percentage

Round the percentage to the nearest tenth. Looking at 72.17, notice that the digit in the hundredths place (7) is 5 or more, so round the tenths place up. Thus, 72.17% rounds to 72.2%.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is a useful skill in math and everyday life. It involves dividing the numerator (the number on top of the fraction) by the denominator (the number on the bottom). This operation gives you a decimal number that represents the same value as the fraction. When you divide the fraction \( \frac{236}{327} \) using a calculator, you obtain the decimal equivalent of approximately \( 0.7217 \). This process is straightforward:

• Take note of the fraction you want to convert.
• Divide the top number by the bottom number using a calculator.
• Record the result as your decimal.

Understanding these steps helps in linking fractions, decimals, and percentages effectively, as they represent the same value in different forms.

Percentage Calculation

Transforming a decimal into a percentage is a common mathematical operation. It involves multiplying the decimal number by 100. This conversion is based on the fact that percent means "per hundred." To continue from our example, convert \( 0.7217 \) to a percentage by performing the following:Multiply:

• Take the decimal \( 0.7217 \).
• Multiply it by 100.
• The result is \( 72.17 \), which means the fraction is equivalent to \( 72.17\% \).

This method allows you to express any decimal value as a percentage which is a more intuitive form for understanding proportions and comparisons.

Rounding Decimals

Rounding numbers is an important skill, especially when dealing with decimals. It helps to simplify figures and make them easier to interpret. When you round a decimal to the nearest tenth, you look at the hundredths place to decide whether to round up or keep the same number.Consider rounding \( 72.17\% \):

• The tenths place number is 1.
• Look at the hundredths place; it is 7, which is 5 or more.
• So, you increase the tenths place by 1, changing \( 1 \) to \( 2 \).
• This rounds \( 72.17\% \) to \( 72.2\% \).

Rounding helps eliminate small, insignificant digits and can clarify the data you're working with.

Educational Math Problem Solving

Solving math problems can sometimes seem daunting, but breaking down each step can make it much more manageable. Problem-solving in mathematics involves understanding what the problem is asking and deciding the best methods to find a solution. For example, converting a fraction to a percentage can be tackled by:

• Identifying the operations needed (division, multiplication).
• Performing each operation carefully, using a calculator if necessary.
• Appropriately rounding the final answer.

By practicing these steps, students develop a structured approach to problem-solving that enhances critical thinking and analytical abilities. This helps not only in math but in other fields as well, fostering a mindset equipped for tackling real-world issues.