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 Question from Emily, a student: What is the grade of the road shown below expressed as a percent rounded to one decimal place? Rise is 40feet Run is 380 feet

Hi Emily,

The slope of a line is a fraction, the "rise" over the "run." Percentage also comes from a fraction, it is the numerator when the denominator is 100. Thus for example if the rise is 40 feet and the run is 500 feet then the slope is

$\frac{40}{500} = \frac{4}{50} = \frac{8}{100} = 8\%.$

If it's not straightforward to find an equivalent fraction with 100 as the denominator you can divide the denominator into the numerator and then multiply by 100. Thus for example if the rise is 9 feet and the run is 47 feet then the slope is

$\frac{9}{47} = 0.1915 = \frac{19.15}{100} = 19.15\%.$

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.