Final answer:
The greatest possible error when measuring to the nearest tenth of a meter is ±0.05 meters. Percent uncertainty is calculated by the greatest possible error divided by the actual measurement, multiplied by 100. Measuring devices' precision and human factors can contribute to measurement uncertainty.
Step-by-step explanation:
Understanding Measurement Uncertainty
When a measurement is taken to the nearest tenth of a meter, the greatest possible error is ±0.05 meters or 5 centimeters. This is because when measuring to the nearest tenth, the actual value could be up to half of the smallest division on the measuring tool above or below the recorded measurement. For example, if something is measured at 2.3 meters, the true length could be anywhere from 2.25 meters to 2.35 meters. The measurement tool's precision and the measurer's skill can impact the uncertainty.
In terms of percent uncertainty, it can be calculated by taking the greatest possible error divided by the measured value and then multiplied by 100. As an illustration, a good-quality measuring tape could be off by 0.50 cm over a distance of 20 m. The percent uncertainty here would be (0.50 cm / 2000 cm) x 100, resulting in a 0.025% uncertainty.
Focusing on the finest divisions that measuring devices can represent, such as millimeters on a ruler or the tenths on a measuring tape, increases precision. Yet, the calibration of the measuring device and human factors, such as eyesight, can introduce additional uncertainty. The challenge lies in minimizing these errors to achieve as accurate a measurement as possible, keeping in mind that some uncertainty is inevitable.