Question

a. Write the equation that is used to calculate percentage error. b. Under what condition will percentage error be negative?

Short answer

a. \( \text{Percentage Error} = \frac{|E - T|}{|T|} \times 100 \)b. The percentage error will be negative if the experimental value is less than the true value.

Step-by-step solution

Understand the Concept of Percentage Error

Percentage error is a way to express the accuracy of a measurement. It compares the difference between the experimental (or measured) value and the true (or theoretical) value as a percentage of the true value.

Write the Equation for Percentage Error

The formula to calculate the percentage error is: \[ \text{Percentage Error} = \frac{|\text{Experimental Value} - \text{True Value}|}{|\text{True Value}|} \times 100 \ \text{or} \ \text{Percentage Error} = \frac{|\text{Measured Value} - \text{Accepted Value}|}{|\text{Accepted Value}|} \times 100 \ \text{or} \ \text{Percentage Error} = \frac{|E - T|}{|T|} \times 100 \] where: - \text{E} is the Experimental Value - \text{T} is the True (or Accepted) Value

Analyze the Sign of Percentage Error

Since the percentage error formula uses absolute values, the result is always positive. However, if the absolute values are removed, the percentage error can be negative. This would happen when the experimental value is less than the true value.

Key concepts

accuracy of measurement

The accuracy of measurement is all about how close your measured value is to the true (or theoretical) value. In simple terms, it shows how 'correct' your measurement is. When you measure something, you want your result to be as close as possible to the actual value.

For example, if you are measuring the length of a table and the actual length is 2 meters, a measurement of 2.1 meters is more accurate than a measurement of 2.5 meters.

Understanding the accuracy of measurement is crucial in experiments and calculations, as it allows you to assess the reliability of your measurements.

experimental value

The experimental value is the value you get from your measurements or experiments. It's what you record during an experiment. This value can vary due to different factors like human error, equipment precision, or environmental conditions.

For instance, if you are experimenting to find the boiling point of water and you record 99°C, this 99°C is your experimental value.

It's essential to compare this experimental value with the theoretical value to determine the accuracy of your measurements.

theoretical value

The theoretical value, also known as the true or accepted value, is the value that is generally accepted by the scientific community. This value is considered to be the 'correct' value based on extensive research and evidence.

For example, the boiling point of water at sea level is 100°C. This 100°C is the theoretical value.

When conducting experiments, you compare your experimental value to this theoretical value to determine how accurate your results are.

negative percentage error

Negative percentage error can occur when the experimental value is less than the theoretical value. It's important to note that the standard formula for percentage error uses absolute values, which makes the result always positive. However, without the absolute values, the formula shows whether the experimental value is above or below the theoretical value.

The formula for percentage error is: \[Percentage Error = \frac{Experimental \, Value - Theoretical \, Value}{Theoretical \, Value} \times 100\]

In this case:
- If the experimental value (E) is less than the theoretical value (T), the percentage error will be negative, indicating an underestimation.