Problem 71 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$2 \frac{1}{2}$$

Step-by-Step Solution

Answer

The number 2 1/2 can be expressed as 250.0% when rounded to the nearest tenth of a percent.

Step 1: Convert to Improper Fraction

The mixed number \(2 \frac{1}{2}\) can be converted to an improper fraction. To do this, multiply the whole number by the denominator and add the numerator: \(2 \times 2 + 1 = 5\). Thus, \(2 \frac{1}{2} = \frac{5}{2}\).

Step 2: Convert Fraction to Decimal

To convert \(\frac{5}{2}\) into a decimal, divide 5 by 2. When you do the division, \(5 \div 2 = 2.5\).

Step 3: Convert Decimal to Percent

To convert the decimal 2.5 into a percent, multiply by 100. So, \(2.5 \times 100 = 250\).

Step 4: Round to the Nearest Tenth of a Percent

Since 250 is a whole number, it can also be expressed as 250.0, which is already rounded to the nearest tenth. Therefore, 250.0% is already at the desired precision.

Key Concepts

Mixed Numbers to Improper Fractions

Converting mixed numbers to improper fractions is a foundational skill in math. A mixed number includes a whole number and a fraction. For example, if you have the mixed number \(2 \frac{1}{2}\), it consists of the whole number 2 and the fraction \(\frac{1}{2}\).

To convert it to an improper fraction, you need to multiply the whole number by the fraction's denominator and then add the numerator. Let's break it down step-by-step:

• Multiply the whole number (2) by the denominator (2): \(2 \times 2 = 4\).
• Add the result to the numerator (1): \(4 + 1 = 5\).

So, \(2 \frac{1}{2}\) becomes \(\frac{5}{2}\). This improper fraction represents the same quantity as the original mixed number but is more convenient for calculations.

Decimal Conversion

Decimal conversion involves turning fractions or other expressions into a decimal format. This is often done to simplify calculations or to prepare for further operations, such as percentage conversion. In our example, we converted \(\frac{5}{2}\) to a decimal.

The process is straightforward:

• Divide the numerator (5) by the denominator (2): \(5 \div 2 = 2.5\).

This division gives you 2.5, which is the decimal form of \(\frac{5}{2}\).

Understanding how to switch between fractions and decimals is valuable. It helps in comparing numbers and performing operations like addition and subtraction more easily.

Rounding Numbers

Rounding numbers helps in presenting data more neatly or reducing the complexity of numerical information. When you're asked to round to the nearest tenth of a percent, you're essentially attempting to simplify a number to one decimal place.

Consider you have the number 250. To express it as a percentage rounded to the nearest tenth, note that:

• As it stands, 250 becomes 250.0% when rounded to one decimal place.

This step is quite straightforward when dealing with whole numbers. For numbers with decimals, you'd look at the digit in the hundredths place to decide whether to round up or down, ensuring precision as required.