How to Deal with Errors in Measurements

What is one common issue when dealing with measurements?

One common issue when dealing with measurements is errors. How can we calculate the true/actual measurements when there is an error present in our data?

Dealing with Errors in Measurements

When errors are present in measurements, it is crucial to address them properly to obtain accurate results. One method to calculate the true/actual measurements is by considering the percentage error and the experimental measurement provided. Let's look at an example:

A student's calculation was found to have a 35.5% error, and his experimental measurement was 15.6 cm. What are the two true/actual measurements?

Calculating True/Actual Measurements

Let's denote the two true/actual measurements as x and y, with x being less than 15.6 cm and y being more than 15.6 cm. We can set up equations to solve for x and y based on the given information:

x + 35.5% of x = 15.6

y - 35.5% of y = 15.6

Converting 35.5% to a decimal, we get 0.355. The equations become:

x + 0.355x = 15.6

y - 0.355y = 15.6

Solving for x:

1.355x = 15.6

x = 15.6 / 1.355 = 11.53 cm

Solving for y:

0.645y = 15.6

y = 15.6 / 0.645 = 24.19 cm

Therefore, the two true/actual measurements are 11.53 cm and 24.19 cm.

It is essential to understand how to handle errors in measurements to ensure the accuracy and reliability of our data.