Describe how the uncertainty in a measured value is determined.

Uncertainty is a quantitative indication of the quality of a measurement that reflects the range of possible values within which the true value of a measured quantity is likely to lie. In other words, uncertainty is an estimate of how much a measured value might deviate from the true value due to various factors involved in the measurement process.

There are several sources of uncertainty in a measurement process, which can be broadly categorized into random and systematic uncertainties. Random uncertainties: - Fluctuations in readings due to unpredictable factors like noise from the environment or the observer's judgment while reading instruments, such as a ruler or a thermometer. - These uncertainties can be reduced by repeating the measurement and taking the average of the results. Systematic uncertainties: - Errors in measurements that consistently occur in one direction (either too high or too low), such as zero-offset in instruments or a wrongly calibrated scale. - Systematic uncertainties cannot be reduced by repeating the measurement, but instead require a correction to the measuring device or technique.

To estimate the uncertainty in a measured value, one can follow these steps: 1. Repeat the measurement several times to obtain a set of data points. 2. Calculate the mean (average) of the data points. 3. Determine the spread of the data points around the mean, either by calculating the range, standard deviation, or using accepted uncertainty values from previous studies or standards. 4. If systematic uncertainties are involved, correct the mean value by accounting for the known or estimated systematic error in the measuring device or technique.

Uncertainty in a measured value is often expressed using the following format: Measured Value ± Uncertainty The uncertainty should be expressed to one or two significant figures, and the measured value should be rounded to the same decimal place as the uncertainty. Example: Suppose you measure the length of an object using a ruler multiple times and obtain the following results: 12.3 cm, 12.5 cm, 12.4 cm, 12.2 cm, and 12.5 cm. From these measurements, the mean value is 12.38 cm, and the range (difference between the highest and lowest values) is 0.3 cm. So you can express the length of the object with its uncertainty as: Length = 12.38 cm ± 0.30 cm