MATH 1012 Section 7.1 U.S. Customary Measurements Bland Above is a chart of common measurements and their relations. In this section we will use these relationships to convert units for problem solving. Converting among Measurement Units 1) Multiply when converting from a larger unit to a smaller unit. 2) Divide when converting from a smaller unit to a larger unit. a) Convert 35 pt to quarts b) Convert 5 1 ft to inches. 2 Converting Using Unit Fractions Choosing a Unit Fraction The numerator should use the measurement unit you want in the answer. The denominator should use the measurement unit you want to change. a) Convert 60 in to feet b) Convert 9 ft to inches. c) Convert 2 days to seconds. d) Convert 448 fl oz to gallons.
MATH 1012 Section 7.2 The Metric System-Length Bland In the metric system we use the meter to measure length. A meter is about 3 inches longer than a yard. This gives you a basic idea of how long a meter is. The metric system is based on 10. Just like our number system and our money. To make longer or shorter length units in the metric system, prefixes are written in front of the word meter. For example, the prefix kilo means 1000, so a kilometer is 1000 meters. The table below shows how to use the prefixes for length measurements. It is helpful to memorize the prefixes because they are also used with weight and capacity measurements. The shaded boxes are the units you will use most often in daily life. We could set up unit fractions and use them to convert between units however, because the metric system is base 10 we can use a simple trick to convert between units. a) Convert 5.70 km to m Counting from the km to the m in the chart on the previous page we count 3 places moving left. So, we will move our decimal 3 places to the right. 5.700 km becomes 5700 m. Notice we added a zero to complete the move. b) Convert 6.9 cm to m Counting from the cm to the m in the chart on the previous page we count 2 places moving right. So, we will move our decimal 2 places to the left. 6.9 cm becomes 0.069 m. Notice we added a zero to complete the move.
MATH 1012 Section 7.3 The Metric System-Capacity, and Weight (Mass) Bland In the U.S. we use gallons to measure capacity, such as milk. In the metric system we use the liter. A liter is about one quart. We convert liter the same way we with meters. Notice the prefixes are the same as meter. a) Convert 3,000 ml to L b) Convert 30.3 L to ml c) A healthy human heart pumps about 65 ml of blood per beat. How many liters of blood does it pump per beat? In the U.S. we use pounds to measure weight. In the metric system we use grams. A dollar bill weighs about a gram. So, we typically use kilograms to weight heavy items. One kilogram weight about 2.2 pounds. To convert between units of grams we follow the same rules as before. a) Convert 0.37 grams to milligrams. b) Convert 15,600 mg to g. c) The average weight of a human brain is 1.45 kg. How many grams is that?
MATH 1012 Section 7.4 Problem Solving with Metric Measurement Bland : Cheddar cheese is on sale at $8.99 per kilogram. Jake bought 350 g of the cheese. How much did he pay, to the nearest cent? The price is $8.99 per kilogram, but the amount Jake bought is given in grams. Convert grams to kilograms (the unit in the price). Then multiply the weight by the cost per kilogram. Convert 350 g to kg. We move to the right 3 times from g to kg on our chart. So, 350 g is equal to 0.35 kg. Now multiply 0.35 kg times the cost per kilogram. So, Jake paid $3.15 for 350 g of cheese. $8.99 0.35 kg = $3.1465 $3.15 1 kg 1 : A miniature Yorkshire terrier, one of the smallest dogs, may weigh only 500 g. But a St. Bernard, the heaviest dog, could easily weight 83 kg. Find the difference in the weights of the two dogs, in kilograms. : A jug of cider contains 3 L. How many 200 ml servings are in one jug?
MATH 1012 Section 7.5 Metric U.S. Customary Conversions and Temperature Bland Until the U.S. has switched completely from customary units to the metric system, it will be necessary to make conversions from one system to the other. Approximate conversions can be made with the help of the table below, in which the values have been rounded to the nearest hundredth or thousandth. ( The only value that is exact, not rounded, is 1 inch = 2.54 cm.) We will use unit fraction to help with conversions. Convert 40 cm to inches. We commonly, have to convert between the two systems. Below are our equations for converting from Fahrenheit to Celsius and from Celsius to Fahrenheit. Convert 68 F to Celsius Convert 15 C to Fahrenheit