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Length Units Conversion: Traditional to Metric, Study notes of Engineering

Bastyr UniversityEngineering

A detailed explanation of length units in both traditional (English) and metric systems. It includes conversion ratios, exercises, and a conversion table. The document aims to help readers understand how to convert between the two systems.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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TABLE OF CONTENTS
Lesson 1 Length – Part I
Lesson 2 Length – Part II
Lesson 3 Length – Part III
Lesson 4 Area
Lesson 5 Volume
Lesson 6 Volume – Cooking and Medications
Lesson 7 Speed – Part I
Lesson 8 Speed – Part II
Lesson 9 Weight
Lesson 10 Temperature
Lesson 11 Fuel Economy
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Download Length Units Conversion: Traditional to Metric and more Study notes Engineering in PDF only on Docsity!

TABLE OF CONTENTS

Lesson 1 Length – Part I Lesson 2 Length – Part II Lesson 3 Length – Part III Lesson 4 Area Lesson 5 Volume Lesson 6 Volume – Cooking and Medications Lesson 7 Speed – Part I Lesson 8 Speed – Part II Lesson 9 Weight Lesson 10 Temperature Lesson 11 Fuel Economy

LESSON 1: LENGTH – PART I

Introduction In 1999, NASA lost a $125 million orbiter because of one simple and seemingly innocuous mistake — the engineering team that built the orbiter used English units of measurements to make their calculations, while the agency responsible for launching the rocket used the metric system. Mistakes like this happen all the time. Since there are two sets of systems that are both widely used, conversion from one system to another has become incredibly important. Whether you are engineering a rocket, calculating the speed of your car, or baking a cake — knowing how to convert from the traditional system to the metric system in your head gives you a huge advantage. In the United States, most measurements are done in traditional (or customary) units, a system of measurements widely used in the United Kingdom and developed from English units. Ironically, even after the United Kingdom switched to the metric system, the United States continues to use the traditional measurement system. There are only three countries in the world — the United States, Liberia, and Burma/Myanmar — that have not yet switched to the International System of Units (SI) metric system as their official system of weights and measures. So, let us start learning to convert between the two systems by beginning with units of length. Vocabulary Before we start learning metric system conversions, we need to learn some terms. Traditional Measures of Length: Metric Measures of Length: Name Abbreviation Name Abbreviation Inch or inches in Millimeter(s) mm Foot or feet ft Centimeter(s) cm Yard or yards yd Decimeter(s) dm Mile or miles mi Meter(s) m Kilometer(s) km Milli - means 1/1000, or one-thousandth Centi - means 1/100, or one-hundredth (remember, one cent is one-hundredth of a dollar) Deci - means 1/10, or one-tenth Kilo - means 1 000 , or one thousand

Converting between Traditional and Metric units Here is what you need to know to convert units from one system to the other system. Remember, in Verbal Math, we round up numbers to simplify calculations. Do not forget to round off! The ratio between inches and centimeters is about 1 inch = 2.54 cm. For practical reasons we will consider 1 in equal to 2.5 cm and use this ratio for our verbal calculation. Hence, 1 in = 2.5 cm 2 in = 5 cm 10 in = 25 cm 20 in = 50 cm and so on... With rounding in mind, there are 0.39 inches in a centimeter, but we will use 0.4 in equal to 1 cm in your calculations. Hence, 1 cm = 0.4 in 2 cm = 0.8 in 5 cm = 2 in 10 cm = 4 in and so on... Here is some more important rounding you should keep in mind: There are 91.44 cm in 1 yard. We will use 1 yd = 90 cm for convenience. There are 30.48 cm in 1 foot. We will use 1 ft = 30 cm. There are 3.2808399 ft in 1 meter, but we will be using 1 m = 3.3 ft.

Conversion Table 1 yd = 3 ft 1 m = 100 cm 1 in = 2.5 cm 1 m = 40 in 1 ft = 12 in 1 m = 3.30 ft 1 ft = 30 cm 1 m = 1.1 yd 1 yd = 0.9 m Exercises - Use the table above to answer these questions How many meters are in 120 cm? Ans: 1.2 m How many meters are in 340 cm? Ans: 3.4 m How many centimeters are in 20 mm? Ans: 2 cm How many meters are in 20 cm? Ans: 0.2 m How many meters are in 5 cm? Ans: 0.05 m How many meters are in 50 cm? Ans: 0.5 m How many meters are in 500 mm? Ans: 0.5 m How many decimeters are in 30 mm? Ans: 0.3 dm How many decimeters are in 80 cm? Ans: 8 dm How many meters are in 9.9 cm? Ans: 0.099 m How many centimeters are in 250 mm? Ans: 25 cm How many meters are in 32 cm? Ans: 0.32 m How many meters are in 51 mm? Ans: 0.051 m How many feet are in 24 in? Ans: 2 ft (there are 12 inches in a foot) How many feet are in 60 in? Ans: 5 ft How many feet are in 120 in? Ans: 10 ft How many feet are in 10 in? Ans:^10 / 12 ft or 5 / 6 ft How many feet are in 25 in? Ans: 2 ft 1 in How many feet are in 50 in? Ans: 4 ft 2 in How many feet are in 6 in? Ans: 0.5 ft , because 12 inches is 1 ft. How many feet are in 126 in? Ans: 10 ft 6 in or 10.5 ft How many feet are in 9 in? Ans: 0. 75 ft (^9 / 12 ft or 3 / 4 ft ) How many feet are in 4 in? Ans: 0.33 ft (^1 / 3 ft ) How many feet are in 8 in? Ans: 0.66 ft

Problems

  1. Beatrice has to cut 1 foot of ribbon but has only a metric ruler. How many centimeters will she need to measure? Ans: about 30 cm
  2. Dion was not sure if 5 in is longer or shorter than 15 cm. Can you help? Ans: 5 in is shorter , because 15 cm is equal to 6 in. Remember that 10 cm are equal to 4 in.
  3. 10 cm were cut off from a 1 ft wire. How long (in inches) is the wire now? Ans: 8 inches left , because 10 cm is equal to 4 in. Remember that 1 ft is equal to 12 inches.
  4. A new 1 / 2 ft long pencil got shortened by 5 cm. How long (in centimeters) is it now? Ans: 10 cm ; if 1 foot is 30 cm , then one-half of it is 15 cm. Next, 1 5 cm - 5 cm = 10 cm.
  5. A plank is 2 feet long. How many cm is that? Ans: 60 cm
  6. Callie's collie is 3 ft long from the tip of his nose to the end of his tail. How much is the pup in centimeters? Ans: 90 cm
  7. How many feet and inches are in 1 meter? Ans: 3 ft and 4 in Solution: 1 m is 100 cm or 40 inches and if there are 12 inches in foot, then 40 inches are equal to approximately 3.3 ft , or 3 ft 4 in.
  8. A pond is 15 ft long. How many meters is that? Ans: 4.5 m , 1 ft is 30 cm or 0.3 m , then 15 ft are equal to 0.3 x 15 = 4.5 ( m ) or 4 m 50 cm. Use Verbal Math when multiplying by 15; first multiply by 10, and then add half of the product: 0.3 x 10 = 3, one-half of 3 is 1.5. Then 3 + 1.5 = 4.5 and our answer.
  9. A whip is 12 ft long. How many meters is that? Ans: 3.6 m (0. 3 m x 12 = 3.6 m )
  10. A door is 8 ft tall. How many meters is that? Ans: 2.4 m
  11. A ceiling is 9 ft tall. How many meters is that? Ans: 2.7 m
  12. A pine tree is 9 meters tall. How many feet is that? Ans: 30 ft Solution: Remember that 3 ft = 90 cm or 0.9 m , then 9 m are 10 times more. If you used the conversion 1 m = 3.3 ft and came up with 29.7 ft answer, it is also correct.
  13. A truck is 1.8 m long. How many feet is that? Ans: almost 6 ft
  14. A TV screen is 60 in across. How many feet is that? What is that in centimeters? Ans: 5 ft , 150 cm
  15. Another TV screen is 40 in across. How much is it in metric measurements? Ans: 1 m
  16. A cord is 72 in long. What is that in ft? What is it in metric units? Ans: 6 ft ; 180 cm (or 1.8 m )
  1. If each guitar is 3 ft long, how long are 6 strings in metric units? Ans: 5.4 m ; if one string is 3 ft or 0.9 m then 6 strings (which are 18 ft ) are 5.4 m.
  2. A ladder is 20 ft long. How long is it in metric units? Ans: 6 m ; if we use 1 ft = 0.3 m conversion.
  3. Jim is taller than Al by 2 ft. How much is that in metric units? Ans: 60 cm or 0.6 m
  4. My well is deeper than my cousin’s by 11 ft. How much is it in metric units? Ans: by 3.3 m ; if 1 ft = 30 cm , then 11 ft = 330 cm , or 3 m 30 cm , or 3.3 m.
  5. A birch tree is 33 ft tall and a pine tree is 42 ft. By how much (in metric units) the pine is taller than the birch? Ans: 2.7 m Solution: A pine is taller than birch by 42 ft – 33 ft = 9 ft. If 1 ft = 30 cm , then 30 cm x 9 = 270 cm or 2.7 m.
  6. We dug 9 ft deep hole and were asked to dig 5 ft deeper. How deep, in metric units, will the new hole be? Ans: 4.2 m
  7. A phone has a reception range of 100 ft. How far is that in metric units? Ans: 30 m
  8. Another phone has a reception range of 100 m. How far is that in feet? Ans: 330 ft ; if 1 m = 3.3 ft , then 100 m = 330 ft
  9. Tony ran 200 m and Yoshi 190 m ran less. How many ft did Yoshi run? Ans: 33 ft
  10. Liam threw a ball 24 meters away. How many feet is that? Ans: almost 80 ft (79.2 ft to be precise) Use Verbal Math when multiplying by 3.3. Because 3.3 x 3 is almost equal to 10, you can multiply the number by 10 and then divide it by 3. Then, 24 x 10 = 240, and then 240 ÷ 3 = 80
  11. A flag pole is 12 m high. How high is it in ft? Ans: about 40 ft (39.6 ft to be more precise) Here is another Verbal Math trick – when multiplying by 3.3, first, multiply by 3, then add 10% of the product; 12 x 3 = 36, next, 10% of 36 is 3.6. Together, 36 + 3.6 = 39.6 and is the answer to the problem.
  12. There are 3 diving boards, one is 1 m , another is 3 m , and the last is 6 m. Approximately how high are these in ft? Ans: 3.3 ft , 9.9 ft (or almost 10 ft ), and 19.8 ft (or almost 20 ft )
  13. Pete’s pony is one and a half meters tall. How tall is it in feet and inches? Ans: 5 ft ; one meter is 40 in and half-a-meter is 20 in. Together, 60 in or 5 ft
  14. Jordan is 6 feet tall. How tall is he in metric units? Ans: 1 m and 80 cm or 1.8 m
  15. Shawn Bradley, the tallest American basketball player, is 7 ft 6 in tall. How tall is he in metric units? Ans: about 225 cm or 2.25 m (the more accurate measurement is 229 cm but in Verbal Math we use approximate numbers).

LESSON 2: LENGTH – PART II

Introduction Understanding how to convert units of length is incredibly important, since they are so often used. Mistakes in converting between units of length are the most common type of conversion error, as there are so many different conversions to remember and we see plenty of both types of measurement in daily life. Think about the different races people compete in – most official races are measured in kilometers. A marathon is measured as 42 kilometers, and we often refer to shorter athletic races as a “10K” or a “5K”. However, when you run on a treadmill or use a special pedometer to measure how far you have run during your practice, it is almost always measured in miles. Confusing! Here are some tables and problems to practice converting units of length. Conversion Table 1 in = 2.5 cm 1 m = 3.3 ft 1 ft = 12 in 1 yd = 3 ft 1 ft = 30 cm 1 yd = 0.9 m 1 m = 100 cm 1 m = 1.1 yd 1 k m = 1000 m 1 m = 40 in Quick Review: 1 centimeter is 10 times longer than a millimeter 1 decimeter is 10 times longer than a centimeter 1 meter is 10 times longer than a decimeter 1 kilometer is 1000 times longer than a meter In other words: Convert distance in centimeters into meters by dividing it by 100, because centi - means 1 / 100. Convert distance in decimeters into meters by dividing it by 10, because deci- means 1 / 10. Convert distance in centimeters into decimeters by dividing it by 10, because there are 10 centimeters in every decimeter. Convert distance in millimeters to meters by dividing it by 1000, because milli- means 1 / 1000. Convert distance in kilometers to meters by multiplying it by 1000, because kilo- means 1000 and there are 1000 meters in each kilometer.

Quick Quiz 2 in = ___ cm? Ans: 5 4 in = ___ cm? Ans: 10 5 in = ___ cm? Ans: 12. 5 cm = ___ in? Ans: 2 , because 1 in = 2.5 cm 10 cm = ___ in? Ans: 4 25 cm = ___ in? Ans: 10 10 in = ___ cm? Ans: 25 100 in = ___ cm? Ans: 250 100 cm = ___ in? Ans: 40 How many centimeters ( cm ) are in 1 meter ( m )? Ans: 100 How many millimeters ( mm ) are in 1 meter ( m )? Ans: 1000 How many millimeters ( mm ) are 1 centimeter ( cm )? Ans: 10 How many millimeters ( mm ) are 1 decimeter ( dm )? Ans: 100 How many millimeters ( mm ) are 1 meter ( m )? Ans: 1000 How many centimeters ( cm ) are in 10 meters ( m )? Ans: 1000 How many centimeters ( cm ) are in 0.1 meter ( m )? Ans: 10 How many meters ( m ) are in 1 centimeter ( cm )? Fun Facts About Meters 1) In addition to be a unit of length, a meter also refers to a special measurement of the arrangement of work in poetry, as well as musical notes. 2) Another meaning of the word meter includes various devices to measure time, speed, flow, time. We also use it words like “postage meter” and “parking meter”, as well as in money and time measuring machines. 3) Since the XIX century, the International Bureau of Weights and Measures in Sevres, France stores a 1 meter bar made of platinum and iridium, which as the prototype of the length unit.

How many centimeters are in 100 decimeters? Ans: 1, How many decimeters are in 1 kilometer ( km )? Ans: 10, 000 because there are 1000 meters in 1 km and there are 10 times as many decimeters. How many inches are in one decimeter? Ans: 4 How many inches are in 1 meter? Ans: 40 How many inches are in 100 meters? Ans: 4, How many inches are in 1 km? Ans: 40, About how many feet are in 1 meter? Ans: about 3.3 (3.28 to be more precise) About how many decimeters are in 1 foot? Ans: 3 About how many feet are in 1 km? Ans: 3, How many yards are in 1 km? Ans: 1, How many meters are in 10 yards? Ans: 9 How many kilometers are in 1,000 yards? Ans: 0. How many decimeters are in 1 yard? Ans: 9 , because there are roughly 90 centimeters in 1 yard. Conversion Table 1 in = 2.5 cm 1 m = 3.3 ft 1 ft = 12 in 1 yd = 3 ft 1 ft = 30 cm 1 yd = 0.9 m 1 m = 100 cm 1 m = 1.1 yd 1 m = 1,000 m 1 m = 40 in

Problems

  1. Inez cut 5.5 dm from a 1 m pipe. How many centimeters were left in? Ans: 45 cm Solution: The answer has to be in centimeters and we need to convert all measurements into this value. Then, 100 cm – 55 cm = 45 cm
  2. Puja wrapped 270 cm of fabric 6 times around her waist. How long was each wrap in ft? Ans: 1.5 ft Solution: If 270 cm were wrapped 6 times, then each wrap was 270 ÷ 6 = 45 ( cm ). Next, 1 ft = 30 cm , which would make 1.5 ft per wrap
  3. Philip stretched a rubber band to 20 cm. How many inches is that? Ans: 8 in Use a Verbal Math trick here – when dividing by 2.5. First, divide by 10, then multiply by 4 (you can also multiply by 4 first and then divide by 10). You can use the trick because you can imagine 2.5 as equal to 10:4. In this problem, 20 ÷ 10 = 2, then 2 x 4 = 8 and your answer
  4. Mercutio’s sword is 36 in long. How many decimeters ( dm ) is that? Ans: 9 dm You can use the trick in reverse when multiplying by 2.5. First, divide by 4, then multiply by 10 (you can also multiply by 10 first and then divide by 4). Here, 36 ÷ 4 = 9, then 9 x 10 = 90 (cm) or 0 dm, the answer to the problem.
  5. Tybalt’s sword is 8 dm long. How long is it in inches? Ans: 32 in Solution: Convert 8 dm into centimeters and then divide that number 2.5.
  6. A bicycle wheel is 700 mm in diameter. How many meters ( m ) is that? Ans: 0.7 m , because there are 1,000 mm in 1 meter.
  7. An earthworm is 170 mm in length. How long is it in decimeters? Ans: 1.7 dm
  8. A snake is 759 mm in length. What is its length in dm? Ans: 7.59 dm
  9. A white hippo’s horn is 1,500 mm. How long is it in inches? Ans: 60 in Solution: The horn is 150 cm and an inch is equal to 2.5 cm. Hence, 150 ÷ 2.5 = 60 ( in )
  10. Donkey’s tail is 1.2 m long. How many millimeters is that? Ans: 1,200 mm
  11. A newborn dolphin is 150 cm long. How many inches long is a baby dolphin? Ans: 60 in
  12. A newborn human baby is only 50 cm long. How many inches is that? Ans: 20 in
  13. A alligator is 75 dm long. How many meters is that? Ans: 7.5 m (the alligator looks less scary if you measure it in meters).
  14. A gibbon can jump 30 ft. How many decimeters can it jump? Ans: 90 dm. There are 30 cm or 3 dm in each foot, then 30 x 3 = 90 ( dm ).