Question

What is meant by a mass measurement expressed in this form: \(4.6 \mathrm{g} \pm 0.2 \mathrm{g} ?\)

Short answer

The mass measurement \(4.6 \text{ g} \pm 0.2 \text{ g}\) indicates an average mass of 4.6 g with a range from 4.4 g to 4.8 g.

Step-by-step solution

Understand the Measurement

The mass measurement given is in the form of an average value and an uncertainty, which means the measurement is not exact. Here, the average mass is represented as 4.6 g.

Identify the Uncertainty

The \(\text{0.2 g}\) in the expression indicates the uncertainty or error margin in the measurement. This tells us how accurate the measurement is and provides a range within which the actual mass likely falls.

Express the Range of Values

Considering both the average mass and the uncertainty, we can say the true mass likely lies within the range of \(4.6 \text{ g} - 0.2 \text{ g} \) and \(4.6 \text{ g} + 0.2 \text{ g}\).

Calculate the Minimum and Maximum Values

Perform the calculations: \(4.6 \text{ g} - 0.2 \text{ g} = 4.4 \text{ g}\) and \(4.6 \text{ g} + 0.2 \text{ g} = 4.8 \text{ g}\).

Key concepts

average mass

When we talk about mass measurements, the term 'average mass' refers to a central value obtained from multiple measurements. This helps to give an idea about the central tendency of the measured data.
For example, in the measurement given as 4.6 g ± 0.2 g, 4.6 grams represents the average mass. This central value is determined by performing several measurements and calculating their mean. By doing so, we obtain a single number that best represents the data collected through measuring the mass of an object multiple times. This average mass allows scientists and students to communicate measurements in a simplified and understandable manner.
Measurements may vary due to different external factors like instrument precision or environmental conditions, so we use the average mass to best represent the true value.

error margin

The error margin, also known as uncertainty, in a mass measurement shows how much the measured value might deviate from the true value. In our example (4.6 g ± 0.2 g), the ± 0.2 g indicates the error margin.
This uncertainty arises due to various factors, such as:

• Instrument precision
• Human error
• Environmental conditions

The error margin gives a range within which the true mass is expected to fall. It provides a sense of the confidence we can have in the measurement. To express this formally, we write it as a plus-minus value (±), signifying the possible variation above and below the measured average.
Understanding and considering the error margin is crucial for accurate scientific measurement and data interpretation.

range of values

The range of values in mass measurement tells us the interval within which the actual mass likely lies. Given the form 4.6 g ± 0.2 g, we calculate the range by adding and subtracting the error margin.
In this example, subtract 0.2 g from 4.6 g to find the minimum value: 4.6 g - 0.2 g = 4.4 g. Then, add 0.2 g to 4.6 g to find the maximum value: 4.6 g + 0.2 g = 4.8 g.
Hence, the range of values is from 4.4 g to 4.8 g.
This means that while the average mass is 4.6 g, the true mass can be as low as 4.4 g or as high as 4.8 g. Recognizing the range helps in better understanding the precision of the measurement and allows for tolerances in scientific and educational experiments.