Problem 106 - Chemistry Matter and Change

Question

Three students use a meterstick with millimeter markings to measure a length of wire. Their measurements are \(3 \mathrm{cm}, 3.3 \mathrm{cm},\) and \(2.87 \mathrm{cm},\) respectively. Explain which answer was recorded correctly.

Step-by-Step Solution

Answer

The 3.3 cm measurement is recorded correctly, matching the meterstick's precision.

Step 1: Identifying the Provided Measurements

The students measured the length of the wire and recorded the measurements as 3 cm, 3.3 cm, and 2.87 cm. We need to determine which measurement is consistent with the precision provided by the meterstick with millimeter markings.

Step 2: Understanding the Precision of the Measurement Tool

A meterstick marked with millimeters can measure lengths with a precision of 0.1 cm, or 1 mm. This means that measurements should be recorded to the nearest millimeter, i.e., to the nearest 0.1 cm.

Step 3: Analyzing Each Measurement

The first measurement of 3 cm implies a precision of 1 cm, which is too imprecise given the tool. The second measurement of 3.3 cm has a precision of 0.1 cm, which aligns with the tool's capabilities. The third measurement of 2.87 cm claims a precision of 0.01 cm, which exceeds the tool's ability and is therefore too precise.

Step 4: Conclusion

The measurement of 3.3 cm is recorded correctly, as it matches the precision achievable with a meterstick that has millimeter markings. It reflects the correct level of precision at 0.1 cm.

Key Concepts

Understanding Measurement Precision

Measurement precision refers to the ability of a tool to measure consistently and accurately. In the context of a meterstick with millimeter markings, precision is crucial.
Imagine a ruler that only has centimeter markings; its precision is quite limited compared to a ruler with millimeter markings. Precise measurements are closer to the true value of what is being measured and lack significant deviation among repeated measurements.

• Precision allows us to have confidence in our measurements by reducing uncertainties.
• It involves measuring quantities to the closest smaller division that the tool allows, which for a millimeter-marked meterstick is 0.1 cm or 1 mm.
• Understanding the tool's limitations is essential not to overstate the precision beyond its actual capability.

Without precise measurements, scientific observations and experiments may yield unreliable results. Thus, choosing the correct degree of precision is key.

The Role of a Meterstick in Measurements

A meterstick is a common measuring tool used to determine length. It's typically made of wood or metal and is marked with millimeter and centimeter divisions, making it a versatile tool for precise measurements.
In our exercise, the students used a meterstick marked at every millimeter, which means they should aim for precision up to 0.1 cm in their records.

• Metersticks provide the scale necessary for determining distances accurately across a wide range of measurements from centimeters to entire meters.
• The millimeter marking allows for more detailed and precise readings, which is particularly important when small deviations can lead to large errors.
• It’s important to align the start of the meterstick directly with the object being measured to avoid parallax errors.

Understanding how to properly use a meterstick can greatly impact the accuracy of the data collected in scientific experiments.

The Importance of Scientific Measurement

Scientific measurement involves using instruments to ensure that observations are accurate, repeatable, and unbiased. In scientific investigations, precision and accuracy are paramount. The goal is to minimize human error and obtain the most reliable data possible.
For instance, scientific measurement with tools like a meterstick requires understanding how the instrument’s precision affects the data.

• Accurate scientific measurement ensures that results are valid and can be compared across different trials and investigations.
• Having precise instruments means that scientific reports and analyses can be replicated by others, fostering reliability in scientific communication.
• Measurements must be expressed accurately, as this influences how results are interpreted and applied in scientific contexts.

Reliable measurement is foundational to the scientific method, making it critical to master its application properly.

Decimal Places in Measurement

Decimal places are pivotal in presenting measurement results with precision. They indicate the level of detail included in a measurement, directly reflecting the instrument's precision capacity. In scientific tools, like a meterstick with millimeter markings, the suitable decimal precision is up to one decimal place (0.1 cm).
When expressing measurements, choosing the appropriate number of decimal places ensures the data's reliability and communicates the right level of certainty.

• In our example, the measurement marked as 3.3 cm signifies a precision of 0.1 cm, correctly representing the meterstick's capability.
• Recorded measurements should never imply greater precision than the measuring tool can provide; otherwise, they mislead about the level of accuracy.
• Using too many decimal places suggests an unrealistic degree of precision, while too few overlook the actual details the tool can capture.

The significance of decimal places lies at the heart of achieved precision, helping refine and validate scientific findings.