Question

Write each fraction as a percent. $$\frac{1}{9}$$

Short answer

Answer: The approximate percentage equivalent of the fraction $$\frac{1}{9}$$ is $$11.\overline{1}\%$$.

Step-by-step solution

Divide the numerator by the denominator

Divide 1 by 9: $$\frac{1}{9} = 0.\overline{1}$$

Multiply by 100 to find the percentage

Multiply the decimal obtained in step 1 by 100: $$0.\overline{1} \times 100 = 11.\overline{1}\%$$

Write the result as a percent

The fraction $$\frac{1}{9}$$ as a percent is approximately: $$11.\overline{1}\%$$

Key concepts

Percent Conversion

Percent conversion is a common method used to express fractions as percentages. When we talk about converting a fraction to a percent, we essentially aim to represent that fraction out of 100.
To perform this conversion for any fraction, the general approach can be summarized in simple steps:

• The first step is to divide the numerator by the denominator. This gives us a decimal.
• Next, take this decimal number and multiply it by 100.
• Finally, add a percent sign (%) to the result. This new value represents the original fraction as a percentage.

In the given exercise with the fraction \(\frac{1}{9}\), after converting to decimal (\(0.\overline{1}\)), multiplying by 100 gives \(11.\overline{1}\%\), converting the fraction into a percentage format.

Decimal Multiplication

Decimal multiplication involves multiplying a decimal by another number, which is crucial when converting decimals into percentages. Let's break down how this works when we multiply any decimal by 100, it moves the decimal point two places to the right.
For instance, if you have a decimal number \(0.\overline{1}\), multiplying it by 100 yields \(11.\overline{1}\).
This process is useful in various mathematical computations, particularly in percent conversion, because percentages represent parts per hundred. Thus, multiplying a decimal by 100 directly translates it into a percentage.
Using calculators or manual calculation, this step is often straightforward and contributes significantly to simplifying fraction-to-percent conversions.

Repeating Decimals

Repeating decimals, also known as recurring decimals, are decimals that have one or more digits that repeat indefinitely. In mathematics, these types of decimals occur when dividing certain fractions.
For example, the fraction \(\frac{1}{9}\) results in a repeating decimal \(0.\overline{1}\). The bar above the '1' — called a vinculum — indicates that it is a repeating sequence.
Dealing with repeating decimals during conversions requires recognizing this repeating pattern.

• It helps to round them appropriately if a precise percentage representation is needed.
• Repetition is a natural part of some decimal fractions.

Understanding them aids in accurately performing operations like percent conversion, ensuring precision in calculations.

Numerator and Denominator Division

The division of the numerator by the denominator forms the backbone of converting fractions to decimals. This division tells us what part of the whole (denominator) is represented by the numerator.
In practical steps:

• The numerator is the top number in a fraction, and the denominator is the bottom number.
• To divide, you determine how many times the denominator fits into the numerator, either exactly or creating a repeating pattern.
• This division process can produce whole numbers, finite decimals, or repeating decimals.

For \(\frac{1}{9}\), dividing 1 by 9 results in \(0.\overline{1}\), a repeating decimal, which then becomes the basis for further calculations, like conversion into a percent. Knowing how to perform this division correctly is crucial for many mathematical applications beyond percent conversion.