Question

2. Ryan is running in a 5-kilometer race. How many feet will he run in the race? Use the conversion rates 5, 280ft = 1mi and 1m i approx 1.61 km. Round to the nearest hundred feet

Answer 1

16,400 ft

Explanation:

You want to know the number of feet in a 5 km race, rounded to the nearest hundred. You are given conversion factors 5280 ft = 1 mi = 1.61 km.

Unit conversion

Unit conversion can be done by multiplying by a conversion factor whose numerator is equal to its denominator, and that cancels unwanted units, replacing them with units you want.

`5\text{ km}=5\text{ km}*\frac{5280\text{ ft}}{1.61\text{ km}}\approx16397.5\text{ ft}\approx\boxed{16,\!400\text{ ft}}`

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Additional comment

Both of the given conversions are equal to 1 mile, so their ratio is 1. We put feet on top of the fraction, because that is the unit we want. The km value is in the denominator so the km units in numerator and denominator cancel.

The conversion for km is 1 mi = 1.609344 km (exactly). The actual conversion to ft will give 16,404 76/381 ft. This has a very long repeating decimal fraction.