Problem 67 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{4}{9}$$

Step-by-Step Solution

Answer

44.4%

Step 1: Convert Fraction to Decimal

Divide the numerator 4 by the denominator 9 to convert the fraction \(\frac{4}{9}\) into a decimal. \(4 \div 9 \approx 0.4444...\). The decimal repeats with the digit 4.

Step 2: Convert Decimal to Percent

To change the decimal \(0.4444...\) to a percent, multiply by 100. Thus, \(0.4444 \times 100 = 44.44\%\).

Step 3: Round to the Nearest Tenth

Round the percent 44.44% to the nearest tenth of a percent. The hundredth place is a 4, which means we leave the tenth place digit (4) unchanged. Thus, it rounds to 44.4%.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction into a decimal is your first step in expressing it as a percentage. This process involves dividing the fraction's numerator by its denominator.
This step helps transform the fraction into a more versatile numerical form. Let’s break it down with the given fraction:

• Identify the numerator and the denominator: For \(\frac{4}{9}\), 4 is the numerator and 9 is the denominator.
• Perform the division: Divide 4 by 9 which gives approximately 0.4444. In division terms, this is read as 4 divided by 9 equaling roughly 0.4444.

The result is a repeating decimal, which means the sequence of numbers will continue interminably. Thus, \(\frac{4}{9}\) converts to a decimal of about 0.4444... Repeating decimals might seem tricky, but they follow a simple pattern that repeats endlessly.

Decimal to Percentage Conversion

Converting a decimal to a percentage is a straightforward process that involves multiplying the decimal by 100. Think of it as asking, "How many parts out of a hundred does this decimal represent?" Here’s how you would convert 0.4444 to a percentage:

• Take the decimal number 0.4444.
• Multiply by 100: \(0.4444 \times 100 = 44.44\%\).

This conversion is based on moving the decimal point two places to the right, effectively showing how many per hundred the value corresponds to. Converting decimals to percentages is a useful method for interpreting values in an everyday and relatable manner.

Rounding Percentages

Rounding numbers helps simplify them, making them easier to use in various contexts. When it comes to percentages, rounding is about finding the closest simpler representation. Consider our percentage, 44.44%:

• Identify the place value to round to: We're rounding to the nearest tenth, so focus on the tenths and hundredths places.
• Examine the hundredths place: It’s 4 in 44.44%.
  • If this digit is 5 or more, you would increase the tenths place by one.
  • If it's less than 5, like in our case, you leave the tenths place unchanged.

So, 44.44% rounds to 44.4%. This step refines the percentage to a more concise form, deploying a figure that’s easy to communicate and work with, without significant loss of precision.