Final answer:
The task is to rewrite the repeating decimal 0.482 with a repeating sequence of 82 as a fraction, which requires algebraic manipulation to express it as a rational number in simplest form.
Step-by-step explanation:
The student has asked to rewrite the decimal 0.482 with a line over 82. This means that we have a repeating decimal where the digits 82 recur indefinitely. The correct way to write this as a fraction is by identifying the repeating sequence and using algebraic methods to convert it into a rational number. This process involves setting the repeating decimal equal to a variable, multiplying by a power of 10 to shift the decimal point, and then subtracting to find an equivalent fraction. The resulting fraction would represent the repeating decimal in simplest form.
To rewrite 0.482 as a fraction, we can put the decimal number over a power of 10. Since 82 is already a power of 10 (10^1), we can write it as a fraction by placing 0.482 over 82 with a line between them, like this Therefore, the rewritten form of 0.482 with a line over 82 is 0.482/82. This process involves setting the repeating decimal equal to a variable, multiplying by a power of 10 to shift the decimal point, and then subtracting to find an equivalent fraction. The resulting fraction would represent the repeating decimal in simplest form.