The Correct Answer and Explanation is:
Correct Answer: 3 feet, 7 and 1/8 inches
Explanation
The task is to convert a measurement given in decimal feet, specifically 3.59 feet (where the ‘ symbol denotes feet), into the more practical and standard format of feet, inches, and a fraction of an inch expressed in eighths. This conversion involves a systematic, step by step process to break down the decimal value into its constituent units.
First, we address the largest unit, which is feet. In the number 3.59, the whole number part is 3. This integer directly represents the number of full feet in the measurement. We can set this value aside as the first component of our final answer. This leaves us with the decimal remainder of 0.59 feet, which must be converted into the smaller units of inches and fractions of an inch.
Next, we convert the remaining 0.59 feet into inches. To do this, we use the fundamental conversion factor that there are 12 inches in a single foot. We multiply the decimal portion of the feet by 12. The calculation is 0.59 multiplied by 12, which equals 7.08. This result means that 0.59 feet is equivalent to 7.08 inches. Following the same logic as before, we take the whole number part of this result, which is 7, as the number of full inches. This gives us the second component of our answer.
Finally, we are left with the new decimal remainder, 0.08 inches. The problem requires us to express this final fraction in terms of eighths of an inch. To determine how many eighths are equivalent to 0.08 inches, we multiply this decimal by 8. The product of 0.08 and 8 is 0.64. This value tells us we have 0.64 eighths of an inch. Since measurement fractions use whole numbers in the numerator (e.g., 1/8, 2/8), we round 0.64 to the nearest whole number. Because 0.64 is closer to 1 than it is to 0, we round up to 1. This gives us the final component: 1/8 of an inch.
By assembling the results from each step, we determine that 3.59 feet is equal to 3 feet, 7 inches, and 1/8 of an inch.
