Reading Measurements

Section 11.2

Objectives

Investigate precision and accuracy of measurements

Explore the use of different measuring devices

New Vocabulary

Accuracy

Precision

Meniscus

A gravitational wave is a ripple in the curvature of spacetime produced by an event involving accelerating masses, such as stars collapsing in space. Albert Einstein predicted these phenomena on the basis of his theory of relativity. Researchers with the Laser Interferometer Gravitational-Wave Observatory (LIGO) found a way to measure gravitational waves. A device called a LIGO detector uses laser beams and mirrors to detect these waves. What units might be used when measuring gravitational waves?

11.2 - Reading Measurements

Measuring Devices

Collection of data is often an important part of answering questions in science. Quantitative data is collected by taking measurements using various scientific tools. Once data has been collected and recorded, it can be organized, analyzed, and evaluated. Data can then be used to make inferences, predict trends, and draw conclusions.

Interpreting and recording measurements properly are key skills in chemistry. Just as adding too much baking soda to a batch of cookie dough affects the taste and texture of the cookies, making poor measurements can affect the outcome of an experiment. Measurement errors can occur for different reasons, including instrument error and human error. It is important that scientists understand how to use measuring tools properly, follow the guidelines for recording values, and report errors.

Figure11.2-1 Measurement errors can affect the outcome of an experiment, just like adding too much baking soda can ruin a cookie.

Many devices are used to make measurements. For example, measuring cups and electric scales like the ones in Figure 11.2-2 portion the ingredients for cooking and baking. In sports, stopwatches report the length of an event or activity. The ruler is a standard tool used to measure lengths of objects. These tools can also be used in a chemistry lab to measure volume, mass, time, and length. Some of the other devices used to make measurements in science are in Table 11.2-1.

Figure11.2-2 Measuring cups and electric scales are used in cooking and baking to portion ingredients for a recipe.

Quantity

Measuring tool

length

ruler, caliper, micrometer

mass

balance

time

clock, stopwatch, analog watch, digital watch

temperature

liquid thermometer, digital thermometer

volume

graduated cylinder, pipette, eudiometer

Table11.2-1 This chart contains some common measuring tools used in science.

These devices indicate a measurement either with a digital display or an analog display. A digital display is an electronic readout that accompanies a measuring device, as shown in Figure 11.2-3. Read measurements directly from an instrument’s digital display. When reporting a measurement taken from a device with a digital display, be sure to report all the digits given by the display, including zeros.

Figure11.2-3 A digital balance measures the mass of an object.

An analog display uses a non-electronic device to indicate the measurement, like a dial, scale, or meter, as shown in Figure 11.2-4. An analog display can present greater challenges in reporting a measurement. Take greater care to report analog measurements properly. Report all the digits of the measurement taken from an analog display known with certainty, and then estimate one more digit.

Figure11.2-4 An analog thermometer measures temperature.

Precision & Accuracy

Precision is how closely a group of measurements agree with one another, which describes the level of exactness of a measurement. Both the tool used to make a measurement and the skill of the measurer affect precision. For example, measuring the length of an eraser with a toothpick is much less precise than measuring the length with a metric ruler. Some specialized instruments have incredibly high levels of precision. A micrometer, as seen in Figure 11.2-5, clamps down on an object, allowing the measurer to determine the object’s thickness with extreme precision. Another device, called a caliper, shown in Figure 11.2-6, precisely measures internal or external lengths between its two heads.

Figure11.2-5 Micrometers make extremely precise measurements of thickness.

A Vernier scale slides over a graduated rectangular main scale, with the help of a thumb screw. The jaws for clasping objects in position are affixed at the left end of the Vernier scale.

Figure11.2-6 Calipers precisely measure internal or external lengths.

A “C” shaped Frame is attached to a Thimble which encompasses a graduated cylindrical sleeve. An anvil and a spindle for clasping objects in position are attached to the inner side of the frame.

Accuracy is often confused with precision. Accuracy describes how close a measurement is to the actual value of the quantity being measured. A measurement can be extremely precise, but not accurate. For example, suppose the label on an unopened package of pencil lead purchased in a store states that its mass is 125 g. However, when the new owner removes the pencil lead from the box and measures it, the scale reads 120.12 g. After some investigation, it is determined that the scale is not calibrated correctly. In this case, the measurement of 120.12 g is very precise, but it is not accurate.

It is also possible for different people to measure the same object with the same measuring device and report different measurements. For example, one person might report the time in Figure 11.2-7 including seconds as 2:49:37 a.m. Another person may record the time as pm instead of am, or record the incorrect hour. Yet another person may record the time without including seconds as 2:49 a.m., or by rounding to 2:50 a.m.

Figure11.2-7 The time displayed by this clock can be reported in different ways.

All measurements have some level of uncertainty, which can come from two different sources. The precision or accuracy of a measurement can be compromised by an instrument’s limitations or by the person using the instrument. Human error is a common source of uncertainty. Knowing how to limit human error in experiments is a valuable skill in scientific investigations.

A measurement made with a device that has a digital display, as shown in Figure 11.2-8, can be read directly from the instrument’s display. When reporting a measurement taken from a device with a digital display, report all of the digits given by the display. The display is designed to indicate values at the appropriate precision for that device. Therefore, the mass of the pen cap is recorded as 0.98 g.

Figure11.2-8 The mass of the pen cap is recorded as 0.98 g.

An analog display, as shown in Figure 11.2-9, can present greater challenges in reporting a measurement. When reporting a measurement taken from a device with an analog display, report all of the digits of the measurement that are known with certainty, and then estimate one more digit. Reporting measurements this way indicates to others the precision of your measuring device. A conservative approach to reading analog displays is to record the nearest marked graduation or halfway between, when appropriate.

Figure11.2-9 The temperature is recorded as 26.0 °C.

Reading Length Measurements

Various devices measure length. A caliper is often used in scale modeling. The caliper, shown in Figure 11.2-10, measures length in three different ways. The outer jaws measure the outside diameter of an object, the inner jaws measure the internal diameter of an object, and the depth probe at the right end measures the depth.

Figure11.2-10 The caliper measures length in three different ways.

A Vernier scale slides over a graduated rectangular main scale, with the help of a thumb screw. Two pairs of jaws for clasping objects in position are affixed on opposite sides, at the left end of the Vernier scale.

A micrometer, as shown in Figure 11.2-11, is often used to make precise measurements in the mechanical engineering and machining industries. Micrometers can also measure the diameter of very large objects, seen through a telescope, or very small objects, seen through a microscope.

Figure11.2-11 A micrometer measures the diameters of very large and very small objects.

A “C” shaped graduated frame is attached to a thimble which encompasses a graduated cylindrical sleeve. An anvil and a spindle for clasping objects in position are attached to the inner side of the frame.

Metric rulers, such as the one in Figure 11.2-12, measure lengths in decimeters, centimeters, or millimeters. The whole numbers on the ruler in Figure 11.2-12 represent centimeters. Each mark represents a tenth of a centimeter, or 1 mm.

Figure11.2-12 Each mark of a metric ruler represents a tenth of a centimeter.

To find the length of an object using a metric ruler, begin by placing the object so that one end lines up with the first mark at the base of the ruler. Then mark the location on the ruler where the tip of the object ends. The ruler markings each represent 0.1 cm. Therefore, the first two digits are certain on a ruler. The third digit is uncertain. Record the first two digits and estimate the third.

Using the outlined steps for measuring with a metric ruler, the screw in Figure 11.2-13 is 0.48 cm. Notice that the end of the screw is between the fourth and fifth markings, which indicates that the first two digits of the measurement are 0.4 cm. Estimate the next digit. Since the end of the screw is closer to the fifth mark than to halfway between the fourth and fifth, record the length as 0.48 cm.

Figure11.2-13 This screw measures 0.48 cm.

Reading Liquid Volume Measurements

Many devices measure volume in the real world and in science, such as measuring cups or graduated cylinders. A pipette, as shown in Figure 11.2-14, is used in laboratories to transport a measured volume of liquid. A eudiometer is a tool used in laboratories to measure the change in volume of a gas mixture.

Figure11.2-14 A pipette is a tool used in laboratories to transport an exact volume of liquid. (photo courtesy of National Cancer Institute)

The pipette has a plunger at one end and a thumb button for releasing liquid. At the other end a thin tube is attached, which extends into a beaker of liquid. Some of the liquid has been aspirated up into the tube.

To determine the volume of a rectangular solid, measure the length, width, and height of the sample with a ruler, caliper, or micrometer and multiply those values together to obtain the volume. When the object is an irregular solid or a liquid, use a different process to determine the volume.

A graduated cylinder measures the volume of a liquid. Begin by obtaining a graduated cylinder large enough to hold the sample. Fill the cylinder with the liquid. The graduated cylinder in Figure 11.2-15 has markings that each represent one milliliter, according to the scale printed along the side. Read graduated cylinder scales from the lowest point of the curved surface of the liquid, which is called the meniscus. Because this is an analog measurement, the first two digits are certain, whereas the third is estimated. Read and record the volume of the liquid to three digits.

Figure11.2-15 A graduated cylinder measures the volume of a liquid at the meniscus.

Using the steps listed above, the sample liquid in Figure 11.2-15 has a volume of 59.5 mL. The meniscus of the liquid is located between 59 and 60 mL so the first two digits must be 59. Estimate the next digit as best you can. Since the meniscus appears halfway between each of these marks, the recorded volume is 59.5 mL.

Reading Mass Measurements

Weight and mass are commonly used interchangeably in the real world, but they actually describe two different properties. The mass of an object indicates the amount of matter it contains, whereas the weight indicates the force of gravity on the object. Because the weight of an object depends on gravitational pull, an object on Earth will weigh more than the same object on the moon. The mass of an object remains the same, regardless of location. The weight of an object can be used to calculate the mass if the effect of gravity is known, like it is on the surface of the Earth.

Various tools measure mass. The most appropriate tool often depends on the size of the object. For example, humans sometimes stand on a bathroom scale, such as Figure 11.2-16, to determine their weight. However, a scale would not be appropriate to measure the weight nor mass of a molecule. A spring scale, such as the one in Figure 11.2-17, is used industrially to weigh heavy loads of material. It is comprised of a spring secured at one end with a hook to attach an object to the other.

Figure11.2-16 A scale can measure the weight of many objects.

Figure11.2-17 A spring scale can measure the weight of large objects.

The base unit for mass is the kilogram in the International System of Units, whereas the newton measures weight. Balances often determine the mass of an object in chemistry and typically report measurements in grams or kilograms. A scale displays a calculation of an object’s mass based on the force it applies. For this reason, scales that report in grams or kilograms are calibrated to account for Earth’s gravity.

Various styles of scales and balances have different capacities and degrees of precision. The simplest of these is a digital scale. Use a digital scale by placing an object on the scale and recording the value displayed.

Figure 11.2-18 shows a triple beam balance, which requires more steps to measure mass than a digital scale. Notice the balance has a pan for holding the object. Find an object’s mass by balancing the object according to the three rails. To do so, first make sure that the balance pan empty and move the three sliders all the way to the left. Next, check to see that the scale reads zero. If it does not read zero, calibrate the balance by using the set screw. Then, place the object on the balance pan and move the weighted sliders until the beam is in the balanced position. The weighted sliders differ to allow for finer degrees of precision in determining the mass of the object. Finally, read the value marked by each slider used and add them to obtain the mass of the object. Record this value as the mass of the object. As an analog display, report digits known with certainty and estimate one additional digit.

Figure11.2-18 A triple beam balance measures the mass of objects in a laboratory.

A pan for holding objects is at one end, on top of three parallel rails which are clasped to the other end of the balance. The pan and the rails are positioned over a supporting platform underneath.

Reading Time Measurements

Various timing devices, such as the clock shown in Figure 11.2-19 or a stopwatch, can record the length of an event or activity. Each timing device has a different degree of precision. Both digital and analog clocks are used in everyday life to get to appointments on time or to track how long it takes to get from one place to another. Physical scientists like chemists often need to measure time.

Figure11.2-19 A clock measures time in both real world settings and in a laboratory.

Measure time on a clock with a few short steps. First, record the time at the start of the event. In chemistry, an event might be a mixture changing color or a substance changing state from liquid to gas. Then, record the time that the event completed. Subtract the start time from the completion time to get the length of time the event lasted.

For example, a chemist might need to record the time it takes for a mixture to change color once a sample is added to it. The chemist should record both the time that a sample liquid is added to the mixture and the time the mixture changed color. Suppose the sample liquid was added at 4:28:00 p.m. and the mixture changed color at 4:32:09 p.m. Subtracting the two measurements results in a time of 4 min and 9 s.