As we learned in the previous section, qualitative observations require the use of the senses to gather data in order to interpret what is happening in our surroundings and then make conclusions based on these interpretations. Quantitative observations gather data by using measurements. From these measurements we can interpret the data and draw conclusions. How exactly do scientists gather all of this numerical data? What kind of equipment is necessary and for what purposes? How accurate is it? Let's take a look, first at some of the typical equipment used in chemistry and then at the skills necessary to determine accuracy and precision. Let's explore the quantitative side of chemistry.
Lesson ObjectivesEdit
 Match equipment type based on the units of measurements desired.
 Determine significant figures of the equipment pieces chosen.
 Define accuracy and precision.
 Distinguish between accuracy and precision.
Equipment Determines the Unit of the MeasurementEdit
Think of the last laboratory experiment that you did. What kind of equipment did you use? If you were measuring out a volume of a liquid, did you use a beaker or a graduated cylinder?
Look at the two figures above; if you were required to measure out 65 mL, what instrument would you most likely want to use? The graduated cylinder has graduations every 10 mL and then further graduations every 5 mL. The beakers could have graduations every 10 mL, 50 mL, or 100 mL depending on which type you use. It would be easier to measure out the volume in a graduated cylinder. What if, in this same lab, you needed to mass out 3.25 g of sodium chloride, NaCl. Look at the two figures below and determine which piece of equipment you would use.
The pan balance measures only to ± 0.1 g. Therefore, you would have to mass out 3.3 g of NaCl rather than 3.25 g. The digital balance can measure to ± 0.01 g. With this instrument you could measure exactly what you need, depending on your skill of course!
The equipment you choose also determines the units in your measurement and vice versa. For example, if you are given graduated cylinders, beakers, pipettes, burettes, flasks, or bottles, you are being asked to measure volume. Volume measurements in the International System of Units use the metric system rather than the imperial system in order to standardize these measurements around the globe. Thus, for volume measurements, we use liters (L) for large volumes and milliliters (mL) for smaller volumes measured in the lab. Look at the figure below and determine what volumes are present in each piece of equipment.
The contrary is also true. What if you were to measure out 5 g of a solid, or 3 cm of wire, or the temperature of a solution; would any of the objects in the figure above be helpful? Why not? These objects are not helpful because these units of measurement are not volumes and all of these pieces of equipment measure volume. For the measurements you need to take, you would need different pieces of equipment. Look at the figure below and match the three required measurements with the pieces of equipment shown.
a) 5 g of a solid
b) 3 cm of wire
c) temperature of a solution
Equipment Determines the Significant FiguresEdit
In the previous section, we looked at a lot of equipment that is used for measuring specific units. The graduated cylinder that measures volume, the balance that measures mass, and the thermometer that measures temperature are a few that we looked at before. We also saw that of two types of balances, one type of balance can more precisely measure mass than the other. The difference between these two balances has to do with the number of significant digits that the balances are able to measure. Remember the pan balance could measure to ± 0.1 g and the digital balance can measure to ± 0.01 g.
Before going any further, what do we recall about significant digits? A measurement can only be as accurate as the instrument that produced it. A scientist must be able to express the accuracy of a number, not just its numerical value.
The instruments that we choose for the laboratory experiments depend on the required amount of accuracy. For example, if you were to make a cup of hot chocolate at home using powdered cocoa, you would probably use a measuring spoon or a teaspoon. Compare this to the requirement of massing out 4.025 g of sodium bicarbonate for a reaction sequence you are doing in the lab. Would the teaspoon do? Probably not! You would need to have what is known as an analytical balance that measures to ± 0.001 g.
Accuracy and PrecisionEdit
Accuracy and precision are two words that we hear a lot in science, in math, and in other everyday events. They are also, surprisingly, two words that are often misused. How often have you heard these terms? For example, you often hear car advertisements that talk about their precision driving ability. But what do these two words mean. Accuracy is how close a number is to the actual or predicted value. If the weatherperson predicts that the temperature on July 1^{st} will be 30 °C and it is actually 29 °C, she is likely to be considered pretty accurate for that day.
Once you have gone into the lab and made measurements, whether they are mass, volume, or length, how do you know if they are correct? Accuracy is the difference between a measured value and the accepted  or what we call the correct  value for that quantity. To improve accuracy, scientists will repeat the measurement as many times as is possible. Precision is a measure of how close all of these measurements are to each other. Therefore, measurements can have precision but not very close accuracy. An example of accuracy of measurements is having the following data: 26 mL, 26.1 mL, and 25.9 mL when the accepted value is 26.0 mL. This data also shows precision. However, if the data had been 25.2 mL, 25.0 mL, and 25.2 mL, they would show precision without accuracy.
Sample Question
Jack collected the following volumes when doing a titration experiment: 34.25 mL, 34.30 mL, 34.60 mL, 34.00 mL, and 34.50 mL. The actual volume for the titration required to neutralize the acid was 34.50 mL. Would you say that Jack's data was accurate? Precise? Both accurate and precise? Neither accurate nor precise? Explain. Solution: All of Jack's data would be accurate because they are close to the true value of 34.50 mL. The data would also be precise having only 2% variance between the highest number and the lowest number. 
The distinction between accuracy and precision and its importance in science is demonstrated in an Annenberg video at Video on Demand – The World of Chemistry – Measurement.
Lesson SummaryEdit
 The task in the experiment determines the unit of measurement; this then determines the piece of equipment. Example: If mass is to be measured, a balance will be chosen as the piece of equipment.
 Conversely, the piece of equipment chosen will determine the unit of measurement. Example: If a graduated cylinder is chosen, the unit of measurement will be volume (mL or L).
 Each piece of equipment has a specified number of significant digits to which it is able to measure. Example: A household thermometer may measure to ± 1 °C or ± 1 °F, where as an ordinary high school alcohol thermometer measures to ± 0.1 °C.
 Significant digits are used in all parts of quantitative measurements in science. Five main rules are provided to read the significant digits of numbers and two main rules for solving algebraic equations maintaining proper significant digits.
 Accuracy is how close the value is to the actual value (remember A and a).
 Precision is how close values are in an experiment to each other. Precision is dependent on the significant digits of the instrument or measurement.
Review QuestionsEdit
 Suppose you want to hit the center of this circle with a paint ball gun. Which of the following are considered accurate? Precise? Both? Neither?
 Four students take measurements to determine the volume of a cube. Their results are 15.32 cm^{3}, 15.33 cm^{3}, 15.33 cm^{3}, and 15.31 cm^{3}. The actual volume of the cube is 16.12 cm^{3}. What statement(s) can you make about the accuracy and precision in their measurements?
 Find the value of each of the following to the correct number of significant digits.
 (a) 1.25 + 11
 (b) 2.308 − 1.9
 (c) 498 − 97.6
 (d) 101.3 ÷ 12
 (e) 25.69 × 0.51
 Why is the metric system used in chemistry?
 Distinguish between accuracy and precision.
 How many significant digits are present in each of the following numbers:
 (a) 0.002340
 (b) 2.0×10^{−2}
 (c) 8.3190
 (d) 3.00×10^{8}
 Nisi was asked the following question on her lab exam. When doing an experiment, what term best describes the reproducibility in your results? What should she answer?
 (a) accuracy
 (b) care
 (c) precision
 (d) significance
 (e) uncertainty
 Karen was working in the lab doing reactions involving mass. She needed to weigh our 1.50 g of each reactant and put them together in her flask. She recorded her data in her data table and began to look at it (Table 3.4). What can you conclude by looking at Karen's data?

Table 3.4 Mass of Reactant 1 Mass of Reactant 2 Trial 1 1.45 ± 0.02 g 1.46 ± 0.02 g Trial 2 1.43 ± 0.02 g 1.46 ± 0.02 g Trial 3 1.46 ± 0.02 g 1.50 ± 0.02 g  (a) The data is accurate but not precise.
 (b) The data is precise but not accurate.
 (c) The data is neither precise nor accurate.
 (d) The data is precise and accurate.
 (e) You really need to see the balance Karen used.

 Find the value of each of the following to the correct number of significant digits.
 (a) 3.567 + 3.45
 (b) 298.968 + 101.03
 (c) 1.25 × 11
 (d) 27 ÷ 5.67
 (e) 423 × 0.1
VocabularyEdit
 accuracy
 How close a number is to the actual or predicted value.
 precision
 How close values are in an experiment to each other.
 significant digits
 A way to describe the accuracy or precision of an instrument or measurement.