### Video Transcript

In an experiment, the density of pure water at sea level on Earth at a temperature of zero degrees Celsius is 997.5 kilograms per meter cubed. Find the percent relative error in the measurement using an accepted value of 1000 kilograms per meter cubed. Give your answer to one decimal place.

We are asked to calculate a percent relative error. We can recall that relative error is defined as the absolute error of a measurement divided by the accepted value for the quantity we are measuring. To use this, we will need to define the absolute error of a measurement. The absolute error is defined as the absolute value of the numerical difference between the measured value and the accepted value.

Now, here, the measured value is 997.5 kilograms per meter cubed, and the accepted value is 1000 kilograms per meter cubed. Therefore, the absolute error is the absolute value of 997.5 kilograms per meter cubed minus 1000 kilograms per meter cubed. Since the two values have the same units, all we need to do is subtract the numbers. 997.5 minus 1000 is negative 2.5. And taking the absolute value, the absolute value of negative 2.5 is just 2.5. So, the absolute error is 2.5 kilograms per meter cubed.

The relative error is then the absolute error 2.5 kilograms per meter cubed divided by the accepted value 1000 kilograms per meter cubed. And to convert this into the percent relative error, we simply multiply by 100. We observe that the units of the numerator, kilograms per meter cubed, are the same as the units for the denominator, kilograms per meter cubed. So, the overall quantity is dimensionless as it should be. Now calculating 2.5 times 100 divided by 1000, we find that the percent relative error is 0.25 percent. And finally, rounding to one decimal place, the answer that we’re looking for is 0.3 percent.