Final answer:
The ratio representing the fractional part of a circle for an 88.6° arc is found by dividing the arc's degrees by the total degrees in a circle, 360, and simplifying the ratio to the lowest terms.
Step-by-step explanation:
To represent the fractional part of a circle using a ratio for an arc of 88.6°, we first recognize that the total number of degrees in a circle is 360. The ratio of the arc to the full circle in degrees is 88.6:360. We can simplify this by dividing both parts of the ratio by their greatest common divisor. To reduce this ratio to lowest terms, we can divide both numbers by 2 until they can no longer be divided by a whole number. So, after dividing by 2 multiple times, we arrive at the reduced ratio of the arc to the whole circle.
For example, if we continue to divide both the numerator and the denominator by 2, we might arrive at a simplified ratio like 443:1800, but this ratio can be simplified further. By finding the greatest common divisor or by continuing to divide by 2, we ultimately reduce the ratio to the lowest terms.
Once the ratio is in its simplest form, that ratio represents the fractional part of the circle corresponding to the 88.6° arc.