To determine the relationship between miles and kilometers, if we use the conversion 39.37 inches= 1 meter, we find that 1 kilometer is approximately equal to 0.62 mile. What if we use the conversion 2.54 centimeters = 1 inch? How far apart are the answers (1 kilometer = x miles) obtained by using the different conversions?

To determine the relationship between kilometers and miles using the conversion 2.54 centimeters = 1 inch, we need to convert both kilometers and miles to centimeters.

1 kilometer is equal to 1000 meters, and since 1 meter is equal to 39.37 inches, we can multiply 1000 by 39.37 to convert kilometers to inches.

1 kilometer = 1000 meters * 39.37 inches/meter = 39,370 inches

Next, we convert inches to centimeters using the conversion 2.54 centimeters = 1 inch. So, multiplying the number of inches by 2.54 gives us the value in centimeters.

39,370 inches * 2.54 centimeters/inch = 99,998.38 centimeters

Now, we need to convert centimeters back into miles. Since 1 mile is equal to 160,934.4 centimeters (approximately), we can divide the number of centimeters by 160,934.4 to get the value in miles.

99,998.38 centimeters / 160,934.4 centimeters/mile = 0.62 miles (approximately)

Comparing this result to the previous conversion using 39.37 inches = 1 meter, we can see that the answer obtained using 2.54 centimeters = 1 inch is also approximately equal to 0.62 miles. So the answers with the two different conversions are the same, with no measurable difference.

To determine the relationship between miles and kilometers using the conversion 2.54 centimeters = 1 inch, we need to convert kilometers to inches using the second conversion factor.

Given that 1 kilometer is equal to 1000 meters, we can use the conversion factor 39.37 inches = 1 meter to convert kilometers to inches. Multiplying 1000 meters by the conversion factor gives us:

1000 meters * 39.37 inches/meter = 39370 inches

Next, we need to convert inches to miles using the second conversion factor. Since 2.54 centimeters is equal to 1 inch, there are 100 centimeters in a meter. So, using the second conversion factor, we can convert inches to centimeters:

39370 inches * 2.54 centimeters/inch = 99792.38 centimeters

Now, we need to convert centimeters to kilometers using the first conversion factor of 1 kilometer = 1000 meters:

99792.38 centimeters * 1 meter/100 centimeters * 1 kilometer/1000 meters = 997.92 kilometers

Finally, we can convert kilometers to miles using the original conversion factor of 1 kilometer = 0.62 mile:

997.92 kilometers * 0.62 mile/kilometer = 618.31 miles (approximately)

Therefore, the answer obtained by using the second conversion (2.54 centimeters = 1 inch) is approximately 618.31 miles. To find the difference between the two answers, we can subtract the two values:

618.31 miles - 0.62 miles = 617.69 miles

So, the two answers obtained by using the different conversions are approximately 617.69 miles apart.

2.54 cm = 1 inch (official definition of inch since 1959)

1 cm = 1/2.54 inches
1 m = 100/2.54 inches

1 km = 1000(100/2.54) inches
= 100000/(2.54*12*5280) miles
= .62137 miles

which is the same as your other definition correct to 2 decimals.