1.2: Measurement and Notation
We need to perform measurements when we observe properties of matter. We express these measurements in standard notations so we can communicate them consistently and easily to others. In this section, we explore how to express measurements in chemistry.
We use a standard set of units, based on the metric system, to perform scientific measurements. Most standard units are their base units (meter) for their property. Note that the base unit for mass (kg) is the only "base" unit with a prefix.
Read this section. Be sure to memorize the SI units of measure listed in the text and the metric prefixes listed in the section "The SI Decimal Prefixes". We will use these units of measure throughout this course, so you need to commit them to memory.
Watch this video which explains the basics of scientific notation. Note that we will discuss Avogadro's Number in more detail in Unit 2.
Next, complete this practice set.
Uncertainty exists in any measured quantity because measurements are always performed by a person or instrument. For example, if you are using a ruler to measure length, it is necessary to interpolate between gradations given on the ruler. This gives the uncertain digit in the measured length. While there may not be much deviation, what you estimate to be the last digit may not be the same as someone else's estimation. We need to account for this uncertainty when we report measured values.
When measurements are repeated, we can gauge their accuracy and precision. Accuracy tells us how close a measurement is to a known value. Precision tells us how close repeat measurements are to each other. Imagine accuracy as hitting the bullseye on a dartboard every time, while precision corresponds to hitting the "triple 20" consistently. Another example is to consider an analytical balance with a calibration error so that it reads 0.24 grams too high. Although measuring identical mass readings of a single sample would mean excellent precision, the accuracy of the measurement would be poor.
Read this text, which text describes how uncertainty comes about in measurements. It uses the example of a dartboard to differentiate between accuracy and precision.
To account for the uncertainty inherent in any measured quantity, we report measured quantities using significant figures or sig figs, which are the number of digits in a measurement you report based on how certain you are of your measurement. Reporting sig figs properly is important, and we need to account for sig figs when performing mathematical calculations using measured quantities. There are rules for determining the number of sig figs in a given measured quantity. There are also rules for carrying sig figs through mathematical calculations.
Watch these two videos to learn how to count sig figs for a given quantity.
Next, watch these two videos. Note that the rules for sig figs for addition and subtraction are different from the rules for sig figs for multiplication and division.
After you watch the videos, complete this practice set.