ACT Science Quiz: Understanding Measurement And Precision

A student times a reaction three times using two different stopwatches. Stopwatch X shows time to the nearest 0.1 s; Stopwatch Y shows time to the nearest 0.01 s. The data table lists the recorded times.

Which measurement set shows the greatest precision?

A burette is a graduated tube that dispenses liquid from a tap at its base, so its scale runs from 0 at the top to larger numbers further down. The scale is marked every 1 mL. A student recorded the level of the bottom of the meniscus before opening the tap and again after closing it. Figure 1 shows both readings.

Based on Figure 1, what volume of solution was delivered from the burette?

A caliper has a fixed main scale marked every 1 mm and a sliding vernier scale whose 10 divisions span 9 mm of the main scale. The whole number of millimetres is read from the main scale mark just before the vernier zero mark, and the tenth of a millimetre is read from whichever vernier division lines up with a main scale mark. Figure 1 shows the two scales of a caliper that is closed on a metal rod.

Based on Figure 1, what is the diameter of the rod?

A student placed a metal block alongside a ruler marked every 0.1 cm, but did not line the left end of the block up with the zero mark. Figure 1 shows the block in position.

Based on Figure 1, what is the length of the block?

The same 25.0 mm gauge block was measured five times by each of three instruments. Precision describes how close repeated measurements of the same object are to one another. Figure 1 plots every measurement.

Based on Figure 1, which instrument is the most precise?

A student wanted to show that three cups of water left in different corners of a room end up at slightly different temperatures. The laboratory thermometer is graduated in tenths of a degree; the classroom thermometer is graduated in whole degrees, and a reading is recorded as the nearest whole degree mark. The student read every cup with both thermometers within a few seconds. Table 1 shows the readings.

Why do the classroom thermometer's readings fail to show that all three cups are at different temperatures?

A well-stirred bath of crushed ice and water sits at 0.0 °C for as long as ice remains in it. A technician checking two thermometers put both into the same ice-water bath and read each of them six times over ten minutes, stirring between readings. Figure 1 shows all twelve readings against the known temperature of the bath.

Which statement about the two thermometers does Figure 1 support?

Four identical rifles were clamped in place and each fired five shots at its own target. A rifle is described as accurate when its shots land near the center of the target, and as precise when its shots land close together, wherever they land. Figure 1 shows the four patterns.

Based on Figure 1, which rifle is precise but not accurate?

The voltmeter in Figure 1 has its smallest scale divisions 0.5 V apart. A reading taken from a marked scale should include every digit that is certain, plus one final digit estimated between the smallest divisions.

Based on Figure 1, which of the following is the most appropriate way to record this voltage?

A student measures the time for a cart to travel a fixed distance using two timing methods. Method 1 uses a handheld stopwatch readable to 0.01 s; Method 2 uses a phone video analyzed frame-by-frame at 30 frames/s (time step $\approx 0.033$ s). The student records one trial from each method.

Which recorded time is most consistent with appropriate precision for the method used?

A student measures the diameter of a wire using a micrometer. The sleeve scale reads $2.5,\mathrm{mm}$, and the thimble aligns at $0.23,\mathrm{mm}$. The micrometer's smallest marked increment on the thimble is $0.01,\mathrm{mm}$, and the student records one estimated digit beyond that increment.

Which recorded diameter is most appropriate?

A student times a reaction using two different stopwatches.

Which measurement shows the greatest precision?

A student measures the same mass five times on a digital balance.

Which statement about measurement precision is supported by the data?

Which measurement shows the least precision in the data set?

A beaker has coarse volume markings every 50 mL. A student reports the volume as 237.6 mL after pouring water into the beaker. Which statement best evaluates this reported measurement based on the instrument's precision?

Four instruments are used to measure the same time interval. Which measurement shows the greatest precision (smallest increment implied by the recorded value)?

Which measurement represents an overestimation of precision?

A student measures 10.0 mL of a solution using a 10 mL graduated cylinder with 0.2 mL markings. The meniscus is shown at 9.8 mL.

Which value is recorded with appropriate precision?

A student records repeated measurements of the same object's length using the same instrument.

The instrument used most likely has a smallest marked division of:

Two instruments are available to measure the diameter of a small bead: (1) a metric ruler with smallest divisions of 1 mm, and (2) a vernier caliper with a vernier scale that allows readings to 0.02 mm.

Which measurement shows the greatest precision (i.e., finest resolution) consistent with the instrument used?