Which method can be used to convert fractions into recurring decimals?

To convert fractions into recurring decimals, one effective method is to find an equivalent fraction with all nines on the bottom. This approach involves recognizing a specific pattern where certain fractions can be represented as repeating decimals based on their denominator.

For instance, when you want to convert a fraction like 1/3 into a decimal, the equivalent fraction of 3/9 demonstrates this conversion clearly. Here, when you divide 1 by 3, you get 0.333..., which indicates a repeating decimal of 3. The presence of nines in the denominator captures the nature of this repeating decimal behavior, where the '3' recurs indefinitely.

This method works particularly well for fractions with denominators that can be expressed in a form leading to repeating decimals. By illustrating the fraction's relationship with nines, students and mathematicians can quickly identify the recurring nature of the decimal without extensive long division or decimal approximation methods.

The other methods, while useful in different contexts, do not inherently provide a direct route to recognizing or establishing the repeating nature of the decimal form of fractions. Multiplying the fraction by 10 shifts the decimal point, common denominators apply to addition or subtraction of fractions, and calculators can provide an approximation but may not always reveal the