Percent Error Made Easy!

The Organic Chemistry Tutor
16 May 201806:25
EducationalLearning
32 Likes 10 Comments

TLDRThis video script provides a clear explanation of how to calculate percent error in experimental measurements, using the example of measuring the density of aluminum and iron. The presenter introduces the formula for percent error, which is the absolute value of the difference between the measured and actual values, divided by the actual value, multiplied by 100. The script walks through two examples: first, calculating the percent error for an aluminum density measurement of 2.6 g/cm³ against an accepted value of 2.7 g/cm³, resulting in a 3.7% error. The second example involves measuring the density of iron at 7.7 g/cm³ against an actual value of 7.8 g/cm³, yielding a 2.036% error. The video also briefly covers how to calculate the simple error, which is the difference between the measured and actual values. The step-by-step process and clear examples make it accessible for viewers to understand the concept of percent error and its calculation.

Takeaways
  • 🧪 The video focuses on calculating percent error in experiments, specifically using the example of measuring the density of aluminum and iron.
  • 📐 The formula for percent error is the absolute value of the difference between the measured and actual values, divided by the actual value, multiplied by 100.
  • 🔍 In the aluminum example, the measured density was 2.6 g/cm³, while the accepted value is 2.7 g/cm³, resulting in a percent error calculation.
  • 📉 The calculated percent error for the aluminum experiment was 3.7%.
  • 📌 To find the simple error, subtract the actual value from the measured value, which in the aluminum example resulted in a negative error, indicating the measured value was below the actual.
  • 🔩 For the iron example, the measured density was 7.7 g/cm³, with the actual density being 7.8 g/cm³.
  • 📝 The error for the iron experiment was calculated as -0.16 g/cm³, indicating the measured value was less than the actual density.
  • 🧮 Using the formula, the percent error for the iron experiment was found to be 2.036%.
  • 📚 The video emphasizes the importance of understanding both the concept of error and how to calculate it, as well as the percent error for accurate experimental results.
  • 🔢 The absolute value is used when calculating percent error to ensure the error percentage is positive regardless of the direction of the error.
  • 🔧 The process demonstrated in the video is applicable to various scientific experiments where comparing measured values to actual or accepted values is required.
Q & A

  • What is the main focus of the video?

    -The main focus of the video is to teach how to calculate percent error in experiments.

  • What is the measured density value of aluminum mentioned in the video?

    -The measured density value of aluminum mentioned in the video is 2.6 grams per cubic centimeter.

  • What is the accepted or actual density of aluminum?

    -The accepted or actual density of aluminum is 2.7 grams per cubic centimeter.

  • What is the formula for calculating percent error?

    -The formula for calculating percent error is the absolute value of the difference between the measured value and the actual value, divided by the actual value, times 100.

  • What is the calculated percent error for the aluminum density experiment?

    -The calculated percent error for the aluminum density experiment is 3.7 percent.

  • How is the error in an experiment defined?

    -The error in an experiment is defined as the difference between the measured value and the actual value.

  • What is the measured density value of iron metal in the second example?

    -The measured density value of iron metal in the second example is 7.7 grams per cubic centimeter.

  • What is the accepted density of iron metal?

    -The accepted density of iron metal is 7.8 grams per cubic centimeter.

  • What is the calculated error for the iron metal density experiment?

    -The calculated error for the iron metal density experiment is -0.16 grams per cubic centimeter.

  • What is the calculated percent error for the iron metal density experiment?

    -The calculated percent error for the iron metal density experiment is 2.036 percent.

  • How does taking the absolute value of the error affect the percent error calculation?

    -Taking the absolute value of the error ensures that the percent error is a positive number, reflecting the magnitude of the error without indicating direction (whether the measured value was above or below the actual value).

  • Why is it important to calculate percent error in scientific experiments?

    -Calculating percent error is important in scientific experiments as it provides a measure of the accuracy of the experimental results compared to the accepted or actual values, indicating how close the experiment was to the expected outcome.

Outlines
00:00
🧮 Calculating Percent Error for Aluminum Density Measurement

This paragraph introduces the concept of calculating percent error with a specific example of measuring the density of aluminum. The measured value is given as 2.6 grams per cubic centimeter, while the accepted value is 2.7 grams per cubic centimeter. The formula for percent error is presented as the absolute value of the difference between the measured and actual values, divided by the actual value, then multiplied by 100. The calculation process is demonstrated step by step, resulting in a percent error of 3.7%. Additionally, the paragraph explains how to calculate the simple error, which is the difference between the measured and actual values. The video script then prompts viewers to attempt a similar calculation for the density of iron metal with given values.

05:02
📐 Calculating Error and Percent Error for Iron Density Measurement

The second paragraph continues the theme of error calculation but applies it to a different context—measuring the density of iron metal. The measured value for iron is provided as 7.7 grams per cubic centimeter, against an actual density of 7.8 grams per cubic centimeter. The error is calculated by subtracting the actual value from the measured value, resulting in a negative 0.1 error. To find the percent error, the absolute value of the error is divided by the actual value and then multiplied by 100. The paragraph demonstrates the calculation process using two formulas, with the second formula being emphasized for its direct application to the given values. The final calculated percent error for the iron density measurement is 2.036%. The paragraph concludes with a note of hope that the video has effectively illustrated the process of calculating percent error.

Mindmap
Keywords
💡Percent Error
Percent error is a measure of the accuracy of a measurement or prediction. It is defined as the absolute value of the difference between the measured value and the actual value, divided by the actual value, and then multiplied by 100. In the video, it is used to assess the accuracy of the density measurements for aluminum and iron metal. For example, the percent error for the aluminum experiment was calculated to be 3.7%.
💡Density
Density is a physical property that represents the mass of a substance per unit volume. It is calculated as mass over volume and is typically expressed in grams per cubic centimeter (g/cm³). In the video, the density of aluminum and iron metal is the subject of the experiments, with the goal of measuring it accurately.
💡Measured Value
The measured value refers to the result obtained from conducting an experiment or taking a measurement. It is the value that is compared to the actual or accepted value to determine the error and percent error. In the script, the measured values for the density of aluminum and iron are 2.6 g/cm³ and 7.7 g/cm³, respectively.
💡Actual Value
The actual value, also known as the true value or accepted value, is the recognized or established figure for a particular measurement. It serves as a benchmark against which the measured values are compared. In the context of the video, the actual density values for aluminum and iron are 2.7 g/cm³ and 7.8 g/cm³.
💡Error
Error, in the context of measurement, is the difference between the measured value and the actual value. It indicates how far off the measurement is from the true value. The video explains how to calculate error as the measured value minus the actual value, such as -0.1 g/cm³ for aluminum and -0.16 for iron.
💡Absolute Value
The absolute value of a number is the non-negative value of that number without regard to its sign. It is used in calculating percent error to ensure the difference is always a positive quantity, regardless of whether the measured value is higher or lower than the actual value. For instance, the absolute value of the error for aluminum is 0.1.
💡Mass
Mass is a fundamental property of matter that represents the amount of matter in an object, typically measured in units like grams. In the video, mass is a component of the density calculation, where it is divided by volume to determine the density of a substance.
💡Volume
Volume is the quantity of space occupied by a substance, typically measured in units like cubic centimeters (cm³). It is the other component in the density calculation, used in conjunction with mass to find the density of a material.
💡Calculator
A calculator is an electronic device used for performing mathematical operations. In the script, it is mentioned as the tool used to perform the calculations for percent error and error, emphasizing the practical aspect of carrying out the calculations.
💡Ideal Value
The ideal value is the expected or desired outcome in an experiment. It is often used as a reference point to assess the performance of an experiment. In the context of the video, the ideal value for the density of aluminum is 2.7 g/cm³, which is the target for the experimental measurement.
💡Experiment
An experiment is a scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact. The video focuses on experiments designed to measure the density of aluminum and iron, highlighting the process of obtaining measured values and comparing them to actual values.
Highlights

The video focuses on calculating percent error in experiments, specifically using the example of measuring the density of aluminum.

The measured value of aluminum density in the experiment was 2.6 grams per cubic centimeter.

The accepted or actual density of aluminum is 2.7 grams per cubic centimeter.

The formula for percent error is given as the absolute value of the difference between the measured and actual values, divided by the actual value, times 100.

The calculated percent error for the aluminum experiment is 3.7%.

The error is simply the difference between the measured and actual values.

In the second example, the measured density of iron metal is 7.7 grams per cubic centimeter, while the actual density is 7.8 grams per cubic centimeter.

The error for the iron metal density measurement is -0.1 grams per cubic centimeter.

The percent error is calculated using the absolute value of the error, divided by the actual value, times 100.

The calculated percent error for the iron metal experiment is 2.036%.

The video provides a step-by-step guide on how to calculate both error and percent error.

The importance of using absolute values in the calculation of percent error is emphasized.

The video demonstrates the application of these calculations in the context of scientific experiments.

The presenter uses a calculator to show the process of calculating percent error, enhancing the clarity of the explanation.

The video is educational and helps viewers understand the concept of percent error in a practical way.

The presenter encourages viewers to pause the video and attempt the calculations themselves, promoting active learning.

The video concludes with a recap of the method for calculating percent error, reinforcing the learning objective.

Transcripts

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Percent ErrorDensity MeasurementExperiment AnalysisAluminum DensityIron DensityScience TutorialError CalculationVideo EducationMeasurement TechniquesPhysical PropertiesScientific Method