Which conversion factors can be used to multiply 4 kilometers/min to get meters per hour

  (1000 m)/(1 km) and (60 min)/(1 h)

Step-by-step explanation:

Put the unit you don't want in a position to cancel the unit in the given number. Write the fraction so that the equivalent amount of the unit you do want is on the other side of the fraction bar.

Here we have km/min with km in the numerator. To cancel that, we need a fraction with km in the denominator. We want meters (m) in the numerator, so we need a fraction that has a number of meters equivalent to 1 km. That will be ...

  (1000 m)/(1 km)

This is one of the conversion factors we will need to multiply by.

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We also have "min" in the denominator. To cancel that, we need a conversion factor with min in the numerator. The unit we want in the denominator is h (hours), so we need an equivalent for hours and minutes. That would be 60 min = 1 h, so we write the conversion factor as ...

  (60 min)/(1 h)

So, our conversion factors are ...

  (1000 m)/(1 km) and (60 min)/(1 h)

The converted number is ...

  (4 km/min)(1000 m/km)(60 min/h) = 240,000 m/h

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Comment on conversion factors

As you can see, we write the fraction so equal amounts are in numerator and denominator. Since the amounts are equal, the value of the fraction is 1. Multiplying by 1 in this form doesn't change the original value, it only changes the units.

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