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 cm, 3.3 cm, and 2.87 cm, respectively. Explain which answer was recorded correctly

Step-by-Step Solution

Answer

Among the three measurements - 3 cm, 3.3 cm, and 2.87 cm - the first and the second measurements are recorded correctly, as they correspond to integer values in millimeters (30 mm and 33 mm, respectively) based on the meterstick with millimeter markings. The third measurement is recorded incorrectly (28.7 mm), as it implies a level of precision that the meterstick can't provide.

Step 1: To convert this to millimeters, we multiply 3 by 10: \(3 \times 10 = 30\) mm. This student's measurements have been expressed as an integer value in millimeters, which is a correct way to record the measurement based on the meterstick with millimeter markings. #Step 3: Analyze the second measurement# The second student's measurement was 3.3 cm.

To convert this to millimeters, we multiply 3.3 by 10: \(3.3 \times 10 = 33\) mm. This student's measurements have been expressed as an integer value in millimeters, which is a correct way to record the measurement based on the meterstick with millimeter markings. #Step 4: Analyze the third measurement# The third student's measurement was 2.87 cm.

Step 2: To convert this to millimeters, we multiply 2.87 by 10: \(2.87 \times 10 = 28.7\) mm. In this case, the measurement is not expressed in integer millimeters; there are decimal places in millimeters. Since the meterstick has only millimeter markings, this level of precision (to the nearest hundredth of a millimeter) is not possible, so the third measurement is recorded incorrectly. #Step 5: Conclusion#

Among the three measurements - 3 cm, 3.3 cm, and 2.87 cm - the first and the second measurements are recorded correctly based on the meterstick with millimeter markings. The third measurement is recorded incorrectly, as it implies a level of precision that the meterstick can't provide.

Key Concepts

Understanding the Meterstick

A meterstick is a common tool used in measurements. It is typically 1 meter long and marked with millimeter and centimeter increments. This allows for measuring lengths with precision up to the nearest millimeter. Understanding how to read these markings is crucial. Each centimeter is divided into 10 millimeters, enabling precise measurements.
When using a meterstick, ensure it is properly aligned with the object whose length you're measuring. Check if the object starts at the zero mark, and ensure you measure straight along the object to avoid parallax errors.

The Importance of Precision in Measurement

Precision in measurement refers to the consistency of repeated measurements. With metersticks, this is governed by the smallest unit of measure visible, which is the millimeter. Measuring precisely means noting the measurement precisely as it appears on the tool, without guessing beyond the smallest scale. Employing the correct unit is essential. Given our meterstick example, expressing lengths using millimeter markings ensures accuracy and precision. The meterstick doesn't mark fractions of a millimeter, so expressing lengths as fractions implies a misconstruing of its precision capabilities.

Mastering Unit Conversion

Unit conversion is a frequent necessity in measurements. It involves changing one unit of measure to another, retaining the same value. For example, converting centimeters to millimeters involves multiplying by 10, as 1 cm equals 10 mm. This is important in maintaining uniformity. If measurements across a project are recorded consistently in millimeters, converting all dimensions to this smallest unit helps compare and combine them easily.
Accurate conversions prevent mistakes that can alter results drastically, highlighting the need for meticulous calculations.

Correct Recording of Measurements

Recording measurements accurately is mandatory for conveying the true length measured. Use the smallest unit marked on your measuring tool, in this case, a millimeter for the meterstick. Ensure clarity and avoid ambiguity by avoiding decimal millimeters if your tool does not allow for such precision. For instance, recording 2.87 cm as 28.7 mm implies a precision not afforded by the meterstick. Always double-check conversions and recorded figures to eliminate errors, ensuring that your measurements hold credibility and are reproducible by others using the same tools.