Question

Write each fraction as a percent. $$\frac{4}{9}$$

Short answer

Question: Convert the fraction $$\frac{4}{9}$$ into a percentage. Answer: Approximately $$44\%$$.

Step-by-step solution

Divide the numerator by the denominator

Divide 4 by 9: $$\frac{4}{9} = 0.\overline{4}$$

Multiply the result by 100

Take the result from Step 1 and multiply by 100 to convert it into a percentage: $$0.\overline{4} \times 100 = 44.\overline{4}\%$$

Round to the nearest whole number (optional)

If necessary, you can round the result from Step 2 to the nearest whole number. In this case, the closest whole number is 44: $$44.\overline{4}\% \approx 44\%$$ So, as a percent, the fraction $$\frac{4}{9}$$ is approximately $$44\%$$.

Key concepts

Division of Fractions

When converting a fraction to a decimal, the key technique is division. A fraction like \( \frac{4}{9} \) represents a division problem itself. The top number, known as the numerator, is \( 4 \), and the bottom number, the denominator, is \( 9 \). To solve \( \frac{4}{9} \), you simply divide \( 4 \) by \( 9 \). This division gives you the decimal \( 0.\overline{4} \), where the bar over the \( 4 \) indicates that it repeats indefinitely. Here's how you can divide to find the decimal:

• Start by writing \( 4 \) as \( 4.000 \). You can continue adding zeros to the right if needed, since it's only extending the division without changing the value.
• Divide \( 4 \) by \( 9 \). Since \( 4 \) is less than \( 9 \), you look at \( 40 \), the result of adding a decimal and a zero.
• \( 9 \) goes into \( 40 \), \( 4 \) times, resulting in a remainder of \( 4 \). Add a zero to the remainder to get \( 40 \) again, repeating the process.

By repeatedly dividing, you find the recurring decimal \( 0.\overline{4} \).It's important to remember that division of fractions simplifies the conversion from fractions to decimals, setting the stage for further steps like converting to percents.

Multiplying Decimals by 100

Once you have a decimal from a fraction, converting it to a percent is straightforward. You take the decimal result and multiply it by \( 100 \). This operation shifts the decimal point two places to the right, transforming the fraction's decimal form into a percentage format.For example, converting \( 0.\overline{4} \) to a percent involves these simple steps:

• Take the decimal \( 0.\overline{4} \).
• Multiply it by \( 100 \), i.e., \( 0.\overline{4} \times 100 \).
• The result is \( 44.\overline{4}\% \), which is the repeated result of moving the decimal two places to the right.

Multiplying by \( 100 \) is essentially shifting the decimal point, making the expression a percentage. The percent sign \( \% \) is used to denote the final result as a percentage, making it clear and recognized universally.This simple multiplication acts as a bridge that takes the decimal, derived from the fraction, transforming it succinctly into a more familiar percentage format.

Rounding Numbers

Rounding is an optional yet crucial step when dealing with decimals. It simplifies the numbers to make them easier to understand or communicate, especially when infinite decimals are involved. In the context of converting fractions to percentages, you often round to the nearest whole number.For \( 44.\overline{4}\% \), here’s the process for rounding:

• Look at the digit immediately following the decimal point. Here, it’s \( 4 \).
• If this digit is \( 5 \) or greater, you would round up. However, since \( 4 \) is less than \( 5 \), the number rounds down.
• The rounded result is \( 44\% \), representative of the whole percentage for most practical purposes.

Rounding simplifies numbers by reducing unnecessary complexity, especially helpful in spoken language or when presenting data.Choosing whether to round depends on the context of where and how the percentage will be used, allowing for easier comparison or reporting in most cases.