# Metric System Basic Units

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Metric System Basic Units
Chapter 3

Original Metric Unit Definitions
A meter was defined as 1/10,000,000 of the distance from the North Pole to the equator. A kilogram (1000 grams) was equal to the mass of a cube of water measuring 0.1 m on each side. A liter was set equal to the volume of one kilogram of water at 4 C. Chapter 3

Another advantage of the metric system is that it is a decimal system. It uses prefixes to enlarge or reduce the basic units. For example: A kilometer is 1000 meters. A millimeter is 1/1000 of a meter. Chapter 3

Metric System Prefixes
The following table lists the common prefixes used in the metric system: Know the common Prefix: k, c, m, µ Chapter 3

Metric Prefixes, continued
For example, the prefix kilo- increases a base unit by 1000: 1 kilogram is 1000 grams The prefix milli- decreases a base unit by a factor of 1000: 1 millimeter is meters Chapter 3

Metric Equivalents We can write unit equations for the conversion between different metric units. The prefix kilo- means 1000 basic units, so 1 kilometer is 1000 meters. The unit equation is 1 km = 1000 m. Similarly, a millimeter is 1/1000 of a meter, so the unit equation is 1 mm = m. Chapter 3

Metric Unit Factors Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers: 1 km or m 1000 m km Since 1 m = mm, we can write the following unit factors. 1 mm or m 0.001 m mm Chapter 3

Metric-Metric Conversions
We will use the unit analysis method we learned in Chapter 2 to do metric-metric conversion problems. Remember, there are three steps: Write down the unit asked for in the answer. Write down the given value related to the answer. Apply unit factor(s) to convert the given unit to the units desired in the answer. Chapter 3

Metric-Metric Conversion Problem
What is the mass in grams of a 325 mg aspirin tablet? Step 1: We want grams. Step 2: We write down the given: 325 mg. Step 3: We apply a unit factor (1 mg = g) and round to three significant figures. 325 mg × = g 1 mg 0.001 g Chapter 3

Two Metric-Metric Conversions
A hospital has 125 liters of blood plasma. What is the volume in milliliters? Step 1: We want the answer in mL. Step 2: We have 125 L. Step 3: We need to convert L to mL: 0.001 mL 1 L . On your own, using dimensional analysis, set up and convert 125 L to mL in your notebook Chapter 3

Metric and English Units
The English system is still very common in the United States All conversion factors are considered constants in our class. The constants have infinite significant digits Chapter 3

Metric-English Conversion
The length of an American football field, including the end zones, is 120 yards. What is the length in meters? Convert 120 yd to meters given that yd = m. 120 yd × = 110 m 1 yd 0.914 m Chapter 3

Compound Units Some measurements have a ratio of units.
For example, the speed limit on many highways is 55 miles per hour. How would you convert this to meters per second? Convert one unit at a time using unit factors. first, miles → meters second, hours → seconds On your own, using dimensional analysis, set up and convert 55 miles per hour to meters per second in your notebook Chapter 3

Volume by Calculation The volume of an object is calculated by multiplying the length (l) by the width (w) by the thickness (t). volume = l × w × t All three measurements must be in the same units. If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters). Chapter 3

Cubic Volume and Liquid Volume
The liter (L) is the basic unit of volume in the metric system. One liter is defined as the volume occupied by a cube that is 10 cm on each side. Chapter 3

Cubic & Liquid Volume Units
1 liter is equal to 1000 cubic centimeters 10 cm × 10 cm × 10 cm = cm3 1000 cm3 = 1 L = 1000 mL Therefore, 1 cm3 = 1 mL. Chapter 3

Cubic-Liquid Volume Conversion
An automobile engine displaces a volume of 498 cm3 in each cylinder. What is the displacement of a cylinder in cubic inches, in3? We want in3; we have 498 cm3. Use 1 in = 2.54 cm three times. = 30.4 in3 × 1 in 2.54 cm 498 cm3 × Chapter 3

Volume by Displacement
If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions. You can determine its volume indirectly by measuring the amount of water it displaces. This technique is called volume by displacement. Volume by displacement can also be used to determine the volume of a gas. Chapter 3

Solid Volume by Displacement
You want to measure the volume of an irregularly shaped piece of jade. Partially fill a volumetric flask with water and measure the volume of the water. Add the jade, and measure the difference in volume. The volume of the jade is 10.5 mL. Chapter 3

The Density Concept The density of an object is a measure of its concentration of mass. It is an inherent property of a pure compound. Density does not change with the size or mass of the compound. Density is defined as the mass of an object divided by the volume of the object. = density volume mass Chapter 3

Density Density is expressed in different units. It is usually grams per milliliter (g/mL) for liquids, grams per cubic centimeter (g/cm3) for solids, and grams per liter (g/L) for gases. Chapter 3

Calculating Density What is the density of a platinum nugget that has a mass of g and a volume of 10.0 cm3 ? Recall, density is mass/volume. = g/cm3 10.0 cm3 g Chapter 3

Temperature Temperature is a measure of the average kinetic energy of the individual particles in a sample. There are three temperature scales: Celsius Fahrenheit Kelvin Kelvin is the absolute temperature scale. Chapter 3

Temperature Scales On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F. On the Celsius scale, water freezes at 0 °C and boils at 100 °C. These are the reference points for the Celsius scale. Water freezes at 273K and boils at 373K on the Kelvin scale. Chapter 3

Temperature Conversions
This is the equation for converting °C to °F. This is the equation for converting °F to °C. To convert from °C to K, add 273. °C = K = °F °C × 100°C 180°F ( ) ( ) 180°F 100°C = °C (°F - 32°F) × Chapter 3

Fahrenheit-Celsius Conversions
Body temperature is 98.6 °F. What is body temperature in degrees Celsius? In Kelvin? K = °C = °C = 310 K ( ) 180°F 100°C = 37.0°C (98.6°F - 32°F) × Chapter 3

Heat Heat is the flow of energy from an object of higher temperature to an object of lower temperature. Heat measures the total energy of a system. Temperature measures the average energy of particles in a system. Heat is often expressed in terms of joules (J) or calories (cal). Chapter 3

Heat vs. Temperature Although both beakers below have the same temperature (100 ºC), the beaker on the right has twice the amount of heat, because it has twice the amount of water. Chapter 3

Specific Heat The specific heat of a substance is the amount of heat required to bring about a change in temperature. It is expressed with units of calories per gram per degree Celsius. The larger the specific heat, the more heat is required to raise the temperature of the substance. Chapter 3