Question

A ruler used to measure a penny has markings every 1 \(\mathrm{mm} .\) Which measurement for the size of the penny is correctly reported for this ruler? $$\begin{array}{llll}{\text { a. } 19.05 \mathrm{mm}} & {\text { b. } 19 \mathrm{mm}} & {\text { c. } 19.1 \mathrm{mm}}\end{array}$$

Short answer

The correctly reported measurement for the penny with a ruler marked in 1 mm increments is 19 mm.

Step-by-step solution

Determine Appropriate Precision

Since the ruler has markings every 1 mm, the measurement can only be accurate to the nearest millimeter. Any measurement more precise than a whole number is not possible with this ruler.

Estimate to the Nearest Marking

Estimate the size of the penny using the ruler to the nearest millimeter. This means that fractional measurements such as 19.05 mm or 19.1 mm cannot be correctly reported since these require more precision than the ruler allows.

Choose the Correct Measurement

The only measurement that matches the ruler's precision is a whole number without decimal places. Therefore, the correct size of the penny reported using this ruler is 19 mm.

Key concepts

Scientific Measurement

Scientific measurement is a fundamental aspect of experimental science. It enables us to acquire data about the world around us in a standardized and replicable manner. To ensure accuracy and consistency in scientific measurements, instruments are used that have a known degree of precision.
When we measure something scientifically, we need to understand two key terms: accuracy and precision. Accuracy refers to how close a measurement is to the true or accepted value, while precision refers to the consistency of repeated measurements. For instance, if we repeatedly measure the length of a table and get 150 cm each time, our measurements are precise.
However, if the true length of the table is actually 155 cm, then our measurements are not accurate. A good scientific measurement is both accurate and precise. Scientists also have to consider significant figures, which refer to the numbers that carry meaning contributing to its precision. This means that the result of any measurement must only be reported to the appropriate level of precision, which is determined by the least precise measuring tool used in the experiment.

Ruler Precision

The precision of a ruler, or any measuring tool, is defined by its smallest increment. For example, if a ruler has markings at every 1 mm, then its precision is 1 mm because that's the smallest distance it can reliably measure between two points.

Understanding Ruler Markings

A ruler marked in millimeters means that any measurement we take can only be as precise as the nearest millimeter. To increase precision, tools with smaller increments, such as a micrometer or a caliper, might be needed. Conversely, if less precision is acceptable, a ruler marked in centimeters would suffice.
To accurately use a ruler, we align one end of the object with the zero mark on the ruler, ensuring we do not suffer from parallax errors by looking at the markings squarely and not at an angle. This also helps improve the reliability of our measurements.

Estimating Measurements

Estimating measurements is a skill that involves approximating the size, length, or quantity of an object when absolute precision is not necessary or when a quick assessment is needed. It can also come into play when the measuring instrument doesn't allow for a more precise measurement.

Techniques in Estimation

When presented with a ruler with 1 mm increments, if an object falls between two markings, we often estimate to the nearest mark. However, because our ruler in the exercise only measures to the nearest millimeter, we cannot truthfully report a measurement with a decimal or fractional part—unless it's a .5 increment which can be typically estimated on the standard ruler.
Moreover, when estimating measurements, we always round to the nearest increment that our measuring tool allows. This ensures that we are not reporting measurements with a false sense of precision that our tool cannot provide. Estimation is essential in scenarios where precise instruments are not available, and a good estimate can provide sufficient information for the purpose at hand.