Numbers 1Preview The lectures in this unit cover an introduction to chemistry and matter, working with numbers and units, and an introduction to atoms and the periodic table. This lecture covers an introduction to scientific notation, units, and number significance. Numbers When collecting information, you may remember that there are two types of observations, Qualitative and Quantitative. (Qualitative is quality-based, such as color, physical state; quantitative is a measurement of an amount or quantity, such as price or mass). This lecture deals with the numbers we use when doing quantitative observations. I. Scientific Notation The first thing we have to address is the fact that in science, we are often faced with really big and really small numbers. For example: Your eyeball contains approximately 12000000 rods (cell appendages which process light) In the process of creating vision, a molecule of rhodopsin in your rods receives a photon of light and creates a product called photorhodopsin in under 0.000000000002 seconds. Because working with very large and very small numbers is common in this class, we need to understand scientific notation – the method scientists use to handle large and small numbers. We do this by splitting up the number into two parts: the numerical value, and the factor of 10 by which it is multiplied (that is, the part that has all the zeroes). For instance, 120000000 rods = 1.2 x 10000000 rods (that is 1.2 x 10 million). Similarly, the photorodopsin product forms in 2 x 0.000000000001 seconds (that is 2 x 1/ 1 trillion) Then we break down the zeroes component into powers of 10, as follows: 101 = 10 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000 104 = 10 x 10 x 10 x 10 = 10000 Note that the power listed (1, 2, 3, 4) directly corresponds to the number of zeroes following the initial 1!Numbers 2Going in the opposite direction: 10-1 = 110 = 0.1 10-2 = 110 * 110 = 1100 = 0.01 10-3 = 110 * 110 * 110 = 11000 = 0.001 Note that the power listed (-1, -2, -3) directly corresponds to the total number of digits that come after the decimal. Using this method, we calculate the power of ten required to get to 10 million or 1/10 trillion by counting the number of digits before or after the decimal. For 10000000, we count 7 zeroes, so 100000000 = 107. So there are 1.2x107 rods in an eyeball. For .000000000001 we count 12 digits past the decimal point. So the time it takes for rhodopsin to form photorhodopsin is 2x10-12 seconds. All you have to do is count digits or zeroes past decimals and you will get the right number! --------------------------------------------------------------------------------------------------------------------- Take a minute to look at your Numbers, Units, & Conversions worksheet and complete section I. This has you practice converting from scientific notation to normal notation, or from normal notation to scientific notation. Do it now while this lecture is fresh! Then look at the answers on the posted key to make sure you can correctly execute this conversion before you move on. -------------------------------------------------------------------------------------------------------------------- II – Units All quantitative measurements have two parts – the number and the unit. No measurement value is complete without the accompanying unit. Measurements may have more than one type of unit associated with them when you see them. Measurements and units include the following: Mass – ex: gram (g), pound (lb), ounce (oz), atomic mass unit (amu) Length – ex: meter (m), foot (ft), inch (in), yard (yd), mile (mi) Time - ex: second (s) Temperature – ex: Kelvin (K), Celsius (°C), Fahrenheit (°F) In each case, the first unit listed is the correct unit employed by the International System (SI units) that has been adopted by most of the world. But since we live in the USA we may be more familiar with the English units of pound, feet, and Fahrenheit. You need to be comfortable using both English and metric units in this class.Numbers 3In addition to the base SI units described above, there are several units that are derived from (developed from) from SI units. Volume is a unit derived from length. It is given as length cubed (width * depth * height of a cube gives volume). One cubic centimeter (cm3 or CC) is a cube with sides that are equal to 1 centimeter long. 1 cm3 = 1 mL (1 milliliter). Liters are the SI unit for volume. Liquids and gases have an easily definable volume: the former is measured with a graduated cylinder, which has markings for volume levels, and the latter is measured as the size of the container holding it. But for solid objects that are not perfect cubes, measurement of volume can be done by measuring the difference in volume when the solid object is added to a fixed amount of water. Density: Derived by mass and volume, according to the formula Density = Mass/Volume. It is commonly given as grams/milliliter for most solid and liquid substances. For gases, it is more appropriate to use grams/liter. III - Metric system prefixes The reason that scientists like the SI units is that they, like scientific notation, generally use a system of base 10. They even have a system of shortcut communication for very large and very small numbers that integrates standard prefixes for certain powers of ten. 1000 meters is 1x103 meters, but the SI community has decreed that the prefix kilo- can be used to stand in for 103. Instead of reporting that we traveled 1000 meters or 1x103 meters, it is convenient to say we traveled 1 kilometer. Note: this only works for a system based on units of 10, i.e. the SI unit system. You would never say you traveled a ‘kilomile’. You must memorize the metric system prefixes given above including the name, symbol, and factor it denotes. You will be required to perform conversions using units with these prefixes throughout the rest of the class.Numbers 4 --------------------------------------------------------------------------------------------------------------------- Before you continue, look at your Numbers, Units, & Conversions worksheet and complete section II. This section has you test yourself on metric system prefixes and their application to simple measurements. Practice while the material is fresh to make sure you understand the concept before you move on!