Convert: 450m/s to m/h.

Question:

Convert: 450m/s to m/h.

Unit Conversion:

A unit conversion process involves changing the units of a given quantity from one to another. This can be done out of convenience for our understanding or more importantly, to make sure calculations are dimensionally consistent. If we want to add, divide, multiply, or subtract two similar quantities (like two speeds or two distances), they have to be in the same units to make sense:

Answer and Explanation:


Let us list all of the conversions we will be using:

  • {eq}\displaystyle 1\ min = 60\ s {/eq}
  • {eq}\displaystyle 1\ h = 60\ min {/eq}


So here what we want to do is make a fraction with either of these two quantities as the numerator and denonimator. This fraction is equal to 1. For example,

{eq}\displaystyle 1 = \frac{1\ min}{60\ s} {/eq}


So we do the conversions as:

{eq}\displaystyle v = 450\ \frac{m}{s} \left(\frac{60\ s}{1\ min} \right)\left(\frac{60\ min}{1\ h} \right) {/eq}

We cancel like units here:

{eq}\displaystyle v = 450\ \frac{m}{\require{cancel}\cancel{s}} \left(\frac{60\ \require{cancel}\cancel{s}}{1\ \require{cancel}\cancel{min}} \right)\left(\frac{60\ \require{cancel}\cancel{min}}{1\ h} \right) {/eq}

We thus get:

{eq}\displaystyle \boxed{v = 1.62\ \times\ 10^6\ \frac{m}{h}} {/eq}


Learn more about this topic:

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Common Unit Conversions

from Business 110: Business Math

Chapter 1 / Lesson 10
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