Section 1.6 Systems of Measurement. A system of measurement is a set of units which can be used to specify any physical attribute of an object.

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1 Section 1.6 Systems of Measurement A system of measurement is a set of units which can be used to specify any physical attribute of an object. There are two systems of measurement used in the United States today. The first is the US Customary System (English System) and the second system of measurement used in the United States is the International System of Units (SI), also called the metric system. The SI system is the universally accepted system for science and trade and commonly used in most of the rest of the world. This system adopts ONE basic standard of measurement for each property (unlike the US Customary System). Basic Units In this section we will look at the fundamental quantities of length, mass and temperature and also the derived quantities of area and volume. The mass of an object is a measure of amount of matter present in an object. The weight of an object refers to the force exerted by gravity on that object. As much as you may want to think these two mean the same thing, they don t. Think of an astronaut s mass and weight on the moon and on the earth. The mass is the same, but the weight is not. Basic Units in the US Customary System The basic unit of temperature in the US Customary System is degrees Fahrenheit. Section 1.6 Systems of Measurement 1

2 Basic Units in the Metric System The basic unit for length in the metric system is the meter (m). The liter (l) is used to measure volume. The term degree Celsius ( o C) is used to measure temperature. The base unit for mass is a gram. Metric Prefixes The metric system creates measuring units of varying magnitudes by adding prefixes to the base units. Each prefix represents multiplying the size of the base unit by a different power of ten. Below are the metric prefixes and the relationship between the different units of length. This same chart can be used for mass or volume if the m for meter is replaced with an l for liter (volume) or a g for gram (mass). You can remember the prefixes using the sentence King Henry Danced Merrily Down Center Main, understanding that the M stands for meter. You d need to change meter to gram or liter if you were not measuring length. Changing Units within the Metric System To move from a smaller unit to a larger unit, move the decimal point one place to the left for each larger unit of measurement until you get to the one you need. To move from a larger unit to a smaller unit, move the decimal point one place to the right for each smaller unit of measurement until you get to the one you need. Section 1.6 Systems of Measurement 2

3 Example 1: Convert: a m to km. b. 14 g to cg. d l to ml e. 240 dal to kl. f. 305 mm to hectometers. g dam to decimeters. Section 1.6 Systems of Measurement 3

4 A basic understanding of the metric system includes an intuitive understanding the size of each metric unit. The following table shows the rough relationship between the units in the metric system and similar units in the US Customary System. Example 2: Which metric length unit (kilometer, meter, centimeter or millimeter) should you use to measure each of the following distances? a. your height b. the width of a human hair c. the distance from Houston to Austin d. the length of your foot Converting Temperature Between Degrees Fahrenheit and Degrees Celsius Formulas: Example 3: You have a high fever of 40 o C. Find the equivalent temperature on the Fahrenheit thermometer. Example 4: The lowest temperature ever recorded in a certain city in the US is -80 o F. Find the equivalent temperature on the Celsius thermometer. Section 1.6 Systems of Measurement 4

5 Area and Volume Area is the amount of space inside a two-dimensional figure. Figure Formula Rectangle A= l w Circle 2 A= π r Volume is the space occupied by a three-dimensional object. Figure Formula Rectangular V = l w h Solid Cylinder 2 V= π rh When calculating area or volume, make sure all dimensions use the same unit, if not, convert. Example 5: What is the storage capacity of a food freezer whose inside measurements are 1.5 meters by 1 meter by 80 centimeters? Try this one: Find the area of a rectangle that is 500 cm by 0.34 hm. Example 6: Find the volume of a cylindrical can with radius 5 cm and height 20 cm. Example 7: Find the area, in square centimeters, of a circular disk with radius 0.12 m. Section 1.6 Systems of Measurement 5