Chapter 2 Data Analysis

Section 1: Units of Measurement

Objectives Define SI base units for time, length, mass, and temperature. Explain how adding a prefix changes a unit. Compare the derived units for volume and density.

SI Units A measurement MUST include both a number and a unit. Since scientists need to report data to other scientists, standard units of measurement are required. The first system of standard units was called the metric system. The revised system used today is called the SI system.

Base Units A base unit is a defined unit based on something in the physical world. There are 7 base units in SI. See pg. 33, Table 1. To better describe a range of possible measurements, scientists add prefixes to base units.

For example If we use the base unit meter, we can develop a range of measurements by using other prefixes with “meter” A millimeter (mm) equals 1/1000 m & would be used to measure the diameter of a drill bit. A kilometer (km) equals 1000 m & would be used to measure the distance between 2 cities.

You must memorize the information given to you in Table 2 on pg. 33 for the following prefixes: kilo, deci, centi, milli

Please note: All prefixes are based on multiples, or factors, of ten. All prefixes can be used with all SI units.

Practice Problems 1 cg = _____ g _____ km = 10 3 m _____ s = 1 ks _____ dg = g 1 mm = _____ m m = _____ mm _____ cg = g ____ s = 1 ds

Derived Units A derived unit is a unit defined by a combination of base units. –The SI unit for speed is m/s. Volume is the space occupied by an object. –The SI unit for volume is m 3. Another oft-used unit for volume is cm 3. Both are used for objects with regular, measurable dimensions.

Practice Problem What is the volume of a piece of metal that measures 10 cm x 5 cm x 2 cm?

Derived Units Volume (cont.) –The metric unit for volume is liter (L). This unit is used for liquids or irregularly-shaped objects. –For smaller quantities, volume is measured in milliliters (mL). 1 L = 1000 mL. * 1 mL = 1 cm 3

Determining Volume for Irregularly-Shaped Objects Use the “water displacement method”. 1-Add water to a graduated cylinder. Record the volume of the water. 2-Carefully place the object in the water in the cylinder.

Determining Volume for Irregularly-Shaped Objects 3-Determine the new volume. 4-Subtract the original volume of the water from the volume of the water plus the object to determine the volume of the object alone.

Practice Problem 30 mL of water is placed in a graduated cylinder. A stone of irregular proportions is placed in the cylinder as well. The volume rises to 37 mL. What is the volume of the stone in cm 3 ?

Derived Units (cont.) Density is the ratio of the mass of an object to its volume. That is, D = m/v. The units generally used for density are g/cm 3 or g/mL. (Remember, 1 mL = 1 cm 3 ) Density is a physical property that can be used to identify unknown materials. For example, every sample of gold will have the same density (19.32 g/cm 3 ) no matter what the size of the sample.

Derived Units (cont.) Density (cont.) –2 grocery bags occupy the same volume. They will feel very different, however, based on what is placed IN the bags. Items of greater mass will create a bag of greater density! –The density of 2 items of the same mass will be greater for the object occupying a smaller space. See Fig. 2-4, pg. 28.

Practice Problems A sample of aluminum has a mass of 13.5 g and a volume of 5.0 cm 3. What is the density of aluminum? A sample of aluminum is placed in 10.5 mL of water. The level of the water rises to 13.5 mL. What is the mass of the aluminum sample? What is the volume of a 20 g sample?

Temperature The temperature of an object is a measure of how hot or cold an object is relative to other objects. A thermometer is a device that will measure temperature. There are 2 temperature scales that scientists use: –the Celsius scale ( 0 C) –the Kelvin scale (K); K is the SI unit.

Temperature To convert between the 2 temperature scales: K = 0 C Practice Problems: ____ K = C 630 K = ____ 0 C ____ K = C