Question

Given that 1 mi = 1760 yd, determine what conversion factor is appropriate to convert 1909 yd to miles.

a) 1/1760 mi/ yd
b) 1760/1 mi/ yd
c) 1909/1 mi/ yd
d) 1/1909 mi/ yd

Answer 1

The correct conversion factor to convert 1909 yards to miles, given that 1 mile = 1760 yards, is a) 1/1760 mi/ yd.

Step-by-step explanation:

To determine the appropriate conversion factor to convert 1909 yards to miles when given that 1 mile = 1760 yards, we use the provided relationship to create a ratio that can be multiplied with the measurement in yards to convert it into miles.

The correct conversion factor would therefore be the reciprocal of the number of yards per mile, which is 1/1760 miles/yard. Using this conversion factor, you multiply the number of yards by this factor to get the measurement in miles.

Here is the step-by-step calculation:

1. Start with the given relationship: 1 mile = 1760 yards.
2. To find the conversion factor from yards to miles, take the reciprocal of yards per mile, which is 1/1760 miles/yard.
3. Multiply the given yard measurement (1909 yards) by this conversion factor:
   1. 1909 yards * (1/1760) miles/yard
   2. This calculation will give the distance in miles.

Therefore, for the student's question, the correct answer is a) 1/1760 mi/ yd.