Math 2303 Section 1.6 Systems of Measurement Two common systems: 1. US Customary System (English System) 2. International System of Units (SI) (Metric System) Basic Measurements We will focus on the following types of measurements.  length  area (derived from length)  volume (derived from length)  weight (mass)  temperature Basic Units: English System  length: inch, foot, yard, mile  area:  volume: , , , , , , acre , , teaspoon ( tsp), tablespoon (tbsp), fluid ounce, cup, pint, quart, gallon  weight : ounce, pound, ton  temperature: degrees Fahrenheit 1 Math 2303 Section 1.6 Metric System  length: meter(centi‐, kilo‐, etc.)  area:  volume: , hectare , liter  weight: gram, tonne  temperature: degrees, Celsius Metric Prefixes kilo (k) hector (h) deka (da) none deci (d) centi (c) milli (m) Popper 01 question 1: Which of the following is not a unit in the metric system? a. centimeter b. liter c. quart d. kilogram Converting Between Metric Units (King Henry danced merrily down central main) Example 1: 2.396m = ________________ cm 2 Math 2303 Section 1.6 Example 2: 40135mg = _________________dag Example 3: 0.0672 kl = _________________ dl Popper 1 questions 2: 83610 cm _______________ hm a. 0.83610 b. 8.3610 c. 83.3610 d. 836.10 Popper 1 question 3: 0.0387 kg _____________ g a. 0.0000387 b. 0.00387 c. 0.387 d. 38.7 Example 4: Given the fact that 1 meter is approximately 39.37 inches, how many inches are in each of the following: a. 1 hectometer b. 1 millimeters 3 Math 2303 Section 1.6 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 5: 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 Popper 1 question 4: Which metric length unit is the most appropriate for measuring the length of a pencil ? a. kilometer b. meter c. centimeter d. millimeter Converting Temperature Between Degrees Fahrenheit and Degrees Celsius Formulas: Example 6: You have a high fever of 40° C. Find the equivalent temperature on the Fahrenheit thermometer. Example 7: The lowest temperature ever recorded in a certain city in the US is ‐80° F. 4 Math 2303 Section 1.6 Find the equivalent temperature on the Celsius thermometer Area and Volume Area is the amount of space inside a two‐dimensional figure. Rectangle: A = l x w Circle : Volume is the space occupied by a three‐dimensional object. Rectangular Sold (Box): A = l x w x h Cylinder: When calculating area or volume, make sure all dimensions use the same unit, if not, convert. Example 8: 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 9: Find the volume of a cylindrical can with radius 5 cm and height 20 cm. Example 10: Find the area, in square centimeters, of a circular disk with radius 0.12 m. 5 Math 2303 Section 1.6 How are weight and mass different?
To understand the differences we need to compare a few points:
1) Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the
pull of gravity on an object.
2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter.
Weight is measured on a scale.
3) The Mass of an object doesn't change when an object's location changes. Weight, on the other hand does
change with location.
Example 11: The approximate mass of objects:
a. The mass of a penny?
b. The mass of an Elephant?
c. The mass of a cell phone?
Popper 1 question 5: Determine the volume of a shipping crate with dimensions in meters: 300cm x 400cm x 600cm a. 72 b. 720
c. 7.2 d. 72
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