# 2: Measurements

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In 1983, an Air Canada airplane had to make an emergency landing because it unexpectedly ran out of fuel; ground personnel had filled the fuel tanks with a certain number of pounds of fuel, not kilograms of fuel. In 1999, the Mars Climate Orbiter spacecraft was lost whilst attempting to orbit Mars because the thrusters were programmed in terms of English units, even though the engineers built the spacecraft using metric units. In 1993, a nurse mistakenly administered 23 units of morphine to a patient rather than the "2–3" units prescribed (the patient ultimately survived). These incidents occurred because people were not paying attention to quantities.

Chemistry, like all sciences, is quantitative. It deals with quantities, things that have amounts and units. Dealing with quantities is very important in chemistry, as is relating quantities to each other. In this chapter, we will discuss how we deal with numbers and units, including how they are combined and manipulated.

• 2.1: Prelude to Measurements
Chemistry, like all sciences, is quantitative. It deals with quantities, things that have amounts and units. Dealing with quantities is very important in chemistry, as is relating quantities to each other. In this chapter, we will discuss how we deal with numbers and units, including how they are combined and manipulated.
• 2.2: Expressing Numbers
Standard notation expresses a number normally. Scientific notation expresses a number as a coefficient times a power of 10. The power of 10 is positive for numbers greater than 1, and negative for numbers between 0 and 1.
• 2.3: Expressing Units
Numbers tell "how much," and units tell "of what." Chemistry uses a set of fundamental units and derived units from SI units. Chemistry uses a set of prefixes that represent multiples or fractions of units. Units can be multiplied and divided to generate new units for quantities.
• 2.4: Significant Figures
Significant figures in a quantity indicate the number of known values plus one place that is estimated. There are rules for which numbers in a quantity are significant and which are not significant. In calculations involving addition and subtraction, limit significant figures based on the rightmost place that all values have in common. In calculations involving multiplication and division, limit significant figures to the least number of significant figures in all the data values.
• 2.5: Converting Units
Units can be converted to other units using the proper conversion factors. Conversion factors are constructed from equalities that relate two different units. Conversions can be a single step or multi-step. Unit conversion is a powerful mathematical technique in chemistry that must be mastered. Exact numbers do not affect the determination of significant figures.
• 2.6: Other Units - Temperature and Density
Chemistry uses the Celsius and Kelvin scales to express temperature. A temperature on the Kelvin scale is the Celsius temperature plus 273.15. The minimum possible temperature is absolute zero and is assigned 0 K on the Kelvin scale. Density relates the mass and volume of a substance. Density can be used to calculate volume from a given mass, or mass from a given volume.
• 2.E: Measurements (Exercises)
These are exercises and select solutions to accompany Chapter 2 of the "Beginning Chemistry" Textmap formulated around the Ball et al. textbook.

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