Question

A student \(10-\mathrm{mL}\) pipet has an uncertainty of \(\pm 0.1 \mathrm{~mL}\) Express the volume of the pipet as an ordinary number.

Short answer

The volume of the pipet is between 9.9 mL and 10.1 mL.

Step-by-step solution

Understanding the Given Values

We are given a pipet volume labeled as \(10\text{-mL}\) with an uncertainty of \(\pm 0.1 \text{ mL}\). This means the exact volume can vary by 0.1 mL from the labeled amount in either direction.

Expressing the Volume Range

To express the volume, we account for the uncertainty, which means we need to find both the maximum and minimum possible volumes. The maximum volume is \(10 + 0.1 = 10.1 \text{ mL}\) and the minimum volume is \(10 - 0.1 = 9.9 \text{ mL}\).

Combining with the Uncertainty

The volume of the pipet can be expressed with its range due to uncertainty as \(10.0 \pm 0.1 \text{ mL}\). This means that any measurement using this pipet could be anywhere from \(9.9 \text{ mL}\) to \(10.1 \text{ mL}\).

Expressing as an Ordinary Number

To express this in simple terms, we present the volume along with its absolute maximum and minimum. Thus, the pipet volume, considering its uncertainty, is simply presented as "between 9.9 mL and 10.1 mL".

Key concepts

Understanding Pipet Volume

When talking about pipet volume, it's important to understand that pipettes are precision tools used in laboratories to measure and transfer small volumes of liquid accurately. In this exercise, the pipet is stated to have a volume of \(10\text{-mL}\). This figure represents the nominal or labeled volume of the pipet, which is the amount of liquid it is designed to dispense if used correctly. However, due to manufacturing limitations, the actual volume may slightly differ every time you use it. Hence, it's crucial to account for this variability, which brings us to the concept of uncertainty.

Calculating the Volume Range

Calculating the volume range is a crucial step in understanding how much a measurement can deviate from its target. In this context, volume range calculation involves adding and subtracting the uncertainty from the nominal volume to find the variation limits. Given a pipet with a nominal volume of \(10\text{-mL}\) and an uncertainty of \(\pm 0.1 \text{ mL}\), you would compute:

• Maximum volume as \(10 + 0.1 = 10.1 \text{ mL}\)
• Minimum volume as \(10 - 0.1 = 9.9 \text{ mL}\)

Therefore, the volume range the pipet can realistically dispense lies between \(9.9 \text{ mL}\) and \(10.1 \text{ mL}\). Recognizing this range is essential for precise scientific work.

Expressing Uncertainty in Measurements

Expressing uncertainty is an integral part of stating measurements in scientific practice. It provides a clearer picture of how precise and accurate your results can be, acknowledging the limitations of measuring instruments. For our pipet, the uncertainty is expressed as \(10.0 \pm 0.1 \text{ mL}\), indicating that the pipet is likely to dispense volumes in this range. A clear statement of this kind allows anyone reading the data to understand the potential variability. Additionally, it underscores the importance of including both your measured value and its inherent uncertainty in reports, ensuring transparency and precision in scientific communication. By displaying values as such, scientists maintain integrity in their work and allow others to properly interpret data.