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6.2.3: Using Metric Conversions to Solve Problems
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- Page ID 62187
- The NROC Project
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Learning Objectives
- Solve application problems involving metric units of length, mass, and volume.
Introduction
Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.
To solve these problems effectively, you need to understand the context of a problem, perform conversions, and then check the reasonableness of your answer. Do all three of these steps and you will succeed in whatever measurement system you find yourself using.
Understanding Context and Performing Conversions
The first step in solving any real-world problem is to understand its context. This will help you figure out what kinds of solutions are reasonable (and the problem itself may give you clues about what types of conversions are necessary). Here is an example.
In the Summer Olympic Games, athletes compete in races of the following lengths: 100 meters, 200 meters, 400 meters, 800 meters, 1500 meters, 5000 meters and 10,000 meters. If a runner were to run in all these races, how many kilometers would he run?
The runner would run 18 kilometers.
This may not be likely to happen (a runner would have to be quite an athlete to compete in all of these races) but it is an interesting question to consider. The problem required you to find the total distance that the runner would run (in kilometers). The example showed how to add the distances, in meters, and then convert that number to kilometers.
An example with a different context, but still requiring conversions, is shown below.
One bottle holds 295 deciliters while another one holds 28,000 milliliters. What is the difference in capacity between the two bottles?
There is a difference in capacity of 1.5 liters between the two bottles.
This problem asked for the difference between two quantities. The easiest way to find this is to convert one quantity so that both quantities are measured in the same unit, and then subtract one from the other.
One boxer weighs in at 85 kilograms. He is 80 dekagrams heavier than his opponent. How much does his opponent weigh?
- \(\ 5 \text { kilograms }\)
- \(\ 84.2 \text { kilograms }\)
- \(\ 84.92 \text { kilograms }\)
- \(\ 85.8 \text { kilograms }\)
- Incorrect. Look at the unit labels. The boxer is 80 dekagrams heavier, not 80 kilograms heavier. The correct answer is 84.2 kilograms.
- Correct. \(\ 80 \text { dekagrams }=0.8 \text { kilograms }\), and \(\ 85-0.8=84.2\).
- Incorrect. This would have been true if the difference in weight was 8 dekagrams, not 80 dekagrams. The correct answer is 84.2 kilograms.
- Incorrect. The first boxer is 80 dekagrams heavier , not lighter than his opponent. This question asks for the opponent’s weight. The correct answer is 84.2 kilograms.
Checking your Conversions
Sometimes it is a good idea to check your conversions using a second method. This usually helps you catch any errors that you may make, such as using the wrong unit fractions or moving the decimal point the wrong way.
A two-liter bottle contains 87 centiliters of oil and 4.1 deciliters of water. How much more liquid is needed to fill the bottle?
The amount of liquid needed to fill the bottle is 0.72 liter.
Having come up with the answer, you could also check your conversions using the quicker “move the decimal” method, shown below.
The amount of liquid needed to fill the bottle is 0.72 liters.
The initial answer checks out. 0.72 liter of liquid is needed to fill the bottle. Checking one conversion with another method is a good practice for catching any errors in scale.
Understanding the context of real-life application problems is important. Look for words within the problem that help you identify what operations are needed, and then apply the correct unit conversions. Checking your final answer by using another conversion method (such as the “move the decimal” method, if you have used the factor label method to solve the problem) can cut down on errors in your calculations.
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LESSON | Converting Units & Solving Problems Involving Conversion
The complete guide to converting units & solving problems involving conversion.
In this post, you'll learn how to solve problems that involve converting units and how to convert measurements from one unit to another in both the English and Metric systems. Since these systems are used by a lot of people, having a good understanding of them will help you solve these problems more accurately. in everyday life.
(toc) Table of Contents
CONVERSION OF MEASUREMENTS FROM ONE UNIT TO ANOTHER
6 steps on how to convert a unit of measurement to another unit.
1. Compare the two units.
2. Find the conversion factors that gives the appropriate ratio to the given unit.
3. Write the conversion as a fraction, where the denominator is in the same unit as the given unit.
4. Write a multiplication problem with the original number and the fraction.
5. Cancel out similar units that appears on the numerator and denominator.
Convert Lengths or Distance
Convert mass, convert area, convert volume, convert time, try this unit conversion calculator.
This unit converter is a free and easy to use tool for converting units of measurements.
It converts length, area, volume, weight, speed, density and temperature. It also converts between different units of measurement.
The converter is available in metric or imperial units. You can type in the unit you want to convert into the search bar or click on the links below to find your desired unit.
Conclusion: Use these Tips to Succeed at Unit Conversions with Ease
When changing from one unit of measurement to another, it is very important to know the table of conversion because this will be your guide.
There are some measurements in the table that can't be changed directly, so we should know which conversion factor is the easiest to use.
You need to know and be good at converting units before you can use the different problem-solving strategies to solve problems that involve converting units.
Unit conversions are a necessary skill in the workplace. Whether you are a student, engineer, or an accountant, you will need to know how to convert units of measurement.
Use these tips to succeed at unit conversions with ease:
- Use a calculator or an online conversion tool.
- Memorize the metric system conversion chart!
- Pay attention to units of measurements in context.
- Think about what units you want and what units you have before starting the conversion process.
- Never forget that there are always two values when converting from one unit to another - one from the original and one from the destination unit!
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Grade 7 Mathematics Module: Solving Problems Involving Conversion of Units
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
This module was designed and written with you in mind. It is here to help you master Solving Problems Involving Conversion of Units. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.
This module is divided into three (3) subtopics, namely:
- Conversion of Measurement from Metric System unit to another Metric System unit and English System unit to another English System unit.
- Conversion of Measurement from Metric System unit to English System unit and vice versa.
- Solving Problems Involving Conversion of Units
After going through this module, you are expected to:
1. convert metric unit to another metric unit;
2. convert English system unit to another English system unit;
3. convert metric unit to English system unit and vice versa; and
4. solve problems involving conversion of units.
Grade 7 Mathematics Quarter 2 Self-Learning Module: Solving Problems Involving Conversion of Units
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Using Metric Conversions to Solve Problems
Learning Objective(s)
· Solve application problems involving metric units of length, mass, and volume.
Introduction
Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.
To solve these problems effectively, you need to understand the context of a problem, perform conversions, and then check the reasonableness of your answer. Do all three of these steps and you will succeed in whatever measurement system you find yourself using.
Understanding Context and Performing Conversions
The first step in solving any real-world problem is to understand its context. This will help you figure out what kinds of solutions are reasonable (and the problem itself may give you clues about what types of conversions are necessary). Here is an example.
This may not be likely to happen (a runner would have to be quite an athlete to compete in all of these races) but it is an interesting question to consider. The problem required you to find the total distance that the runner would run (in kilometers). The example showed how to add the distances, in meters, and then convert that number to kilometers.
An example with a different context, but still requiring conversions, is shown below.
This problem asked for the difference between two quantities. The easiest way to find this is to convert one quantity so that both quantities are measured in the same unit, and then subtract one from the other.
Checking your Conversions
Sometimes it is a good idea to check your conversions using a second method. This usually helps you catch any errors that you may make, such as using the wrong unit fractions or moving the decimal point the wrong way.
Having come up with the answer, you could also check your conversions using the quicker “move the decimal” method, shown below.
The initial answer checks out—0.72 liter of liquid is needed to fill the bottle. Checking one conversion with another method is a good practice for catching any errors in scale.
Understanding the context of real-life application problems is important. Look for words within the problem that help you identify what operations are needed, and then apply the correct unit conversions. Checking your final answer by using another conversion method (such as the “move the decimal” method, if you have used the factor label method to solve the problem) can cut down on errors in your calculations.
Solve Problems Involving the Calculation and Conversion of Units of Measure, Using Decimal Notation Up to 3 D.P. Where Appropriate
When solving problems involving calculation of units of measure, it is helpful to know our conversion facts.
When adding and subtracting mixed units of measure, it helps to convert our measures to the same units first.
When solving measure problems that involve multiplication or division, we don’t always need to convert our measures straight away. Often it is easier to do so after the calculation in order to give the answer in the correct unit of measure.
Example 1 => 4.25km + 1500m = ? When adding mixed units of measure to solve a problem, it usually helps converting your measures to the same unit before calculating => 4.25km + 1500m =4.25km + 1.5km = 5.75km
Example 2 => 7.5kg – 3250g = ? When subtracting mixed units of measure to solve a problem, it helps to convert your measures to the same unit before calculating => 7.5kg – 3250g =7.5kg – 3.25kg = 4.25kg
Example 3 => An empty case weighs 7000g. Izzy packs 14.125kg of clothing inside. How much does the suitcase now weigh in kilograms? Solving an addition or subtraction measure word problem often needs a conversion first before a calculation. 7000g = 7kg. 14.125kg + 7kg = 21.125kg.
Example 4 => A small jar of fish food holds 15g. How much food would there be in 125 pots in kilograms? With x and ÷ word problems, often it is not necessary to convert units before the calculation. We often need to convert our answers to the correct unit after the calculation. 15g x 125g = 1875g. Converting to kg gives us an answer of 1.875kg.
Now try a few practice questions!
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Dec 15, 2024 · Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.
6 Steps on How to Convert A Unit of Measurement to Another Unit 1. Compare the two units. 2. Find the conversion factors that gives the appropriate ratio to the given unit. 3. Write the conversion as a fraction, where the denominator is in the same unit as the given unit. 4. Write a multiplication problem with the original number and the ...
In this lesson, you will learn how to solve problems involving conversion of units and its prerequisite skill which is the conversion of measurements from one unit to another in both Metric and English systems. Since these systems are widely used in our community, a good grasp of the concept will help you to be more accurate in solving these ...
Conversion of Measurement from Metric System unit to English System unit and vice versa. Solving Problems Involving Conversion of Units; After going through this module, you are expected to: 1. convert metric unit to another metric unit; 2. convert English system unit to another English system unit; 3. convert metric unit to English system unit ...
I. Units of measurement A. Units of measurement in any system can be divided into three major categories: units that measure mass, units that measure length (size), and units that measure volume (quantity). Metric is no different. In the metric system, each measurement area has a standard base unit used to define the volume, length, or mass of a
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When solving problems involving calculation of units of measure, it is helpful to know our conversion facts. When adding and subtracting mixed units of measure, it helps to convert our measures to the same units first. When solving measure problems that involve multiplication or division, we don’t always need to convert our measures straight ...
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