4.8: Converting Metric Units
Introduction
The Computer Game
Before leaving the science museum, Caleb found a really cool computer game all about metrics. Caleb had been practicing his metric conversions while playing at the Metric Playground, but now it was time for him to apply what he had learned.
The object of the game is to move the mountain climber up the mountain by solving problems involving metric lengths, weights and liquids. Each time a correct answer is given, the mountain climber moves up the mountain. You keep playing until the climber reaches the top.
At the beginning of the game, Caleb sees this problem on the computer screen. It is a problem that requires Caleb to use greater than or less than symbols to compare values.
5.5 grams _____ 4500 mg
Caleb is unsure of the correct answer. He decides to skip this problem by pushing the NEXT button on the computer.
Here is Caleb’s second problem.
6.7 Liters \begin{align*}\times\end{align*} 10 = _____
Caleb thought that the answer was 6700 so he entered that answer into the computer.
TRY AGAIN popped up on his screen.
Finally Caleb decided to try one more problem.
______ kilograms is one hundred times lighter than 1550 kilograms
Caleb is stuck again.
You can help Caleb. In this lesson you will learn all about comparing metric units of length, mass and capacity. You will also learn to convert units using powers of ten.
What You Will Learn
In this lesson, you will learn the following skills:
- Convert metric units of length, mass and capacity using powers of ten.
- Compare and order given metric measurements of length, mass or capacity.
- Solve real-world problems involving conversion of metric measures of length, mass and capacity.
Teaching Time
I. Convert Metric Units of Length, Mass and Capacity Using Powers of Ten
This section combines a couple of different skills that we have already learned. We have learned all about metrics and about how to convert metric units of length, mass and capacity. We have also learned how to multiply decimals using powers of ten such as 10, 100, 1000.
How can we put these two skills together?
We can put them together by converting metric units using powers of ten. This will require us to move the decimal point as we did in earlier lessons. Let’s look at an example.
Example
Convert 150 cm into mm by multiplying by a power of ten.
We know that there are 10 mm in 1 cm. When we go from a larger unit to a smaller unit we multiply. Therefore, we are going to multiply 150 cm by 10.
150 cm \begin{align*}\times\end{align*} 10 \begin{align*}=\end{align*} _____ mm
We know that when we multiply by 10 we move the decimal point one place to the right. The decimal point in a whole number is after the number. So we need to add a zero placeholder to 150.
150 cm = 1500 mm
We can do this when we convert from a smaller unit to a larger unit too. Let’s look at this one involving capacity.
Example
1250 milliliters = _____ L
We know that there are 1000 milliliters in one liter. We need to divide 1250 milliliters by 1000. To do this, we will move the decimal point three places to the left. The decimal point is after the number in a whole number.
1250 milliliters = 1.25 Liters
We can complete this with any unit of measure as long as we know the conversion equivalents and remember how to use powers of ten to move the decimal point to the left or to the right.
Here are a few for you to try.
- 1340 ml = _____ Liters
- 66 grams = _____ mg
- 1123 m = _____ km
Take a few minutes to check your work with a peer.
II. Compare and Order Given Metric Measurements of Length, Mass or Capacity
In a previous lesson, we learned that we can have metric units that are equivalents of each other. For example, 100 cm is equal to 1 meter. Because of this, 500 cm is equal to 5 meters. What if we have different metric units and different quantities?
How can we compare metric units?
To compare metric units, we have to use comparisons between the numbers. Let’s look at an example.
Example
4.5 m _____ 500 cm
We have two different metric units here. We have centimeters and we have meters. We can compare the units by thinking about the equivalents. If there are 100 centimeters in one meter, then 500 cm is the same as 5 meters. 5 meters is greater than 4.5 meters.
4.5 m < 500 cm
We can work this way with metric units of length, mass and capacity.
Example
7.6 kg _____ 7800 g
Which is greater? To figure this out, we need to use the equivalents that we have already learned. There are 1000 grams in 1 kg. Therefore, 7800 grams becomes 7.8 kilograms.
We know from our work with decimals that 7.6 is less than 7.8. Now we can compare them.
7.6 kg < 7800 g
Take a minute to compare a few of these on your own.
- 6.5 kg _____ 50000 g
- 500 mL _____ .5 liters
- 7000 m _____ 7.1 km
Take a few minutes to check your work with a peer.
Real Life Example Completed
The Computer Game
Now we are ready to help Caleb with his computer game. Here is the problem once again.
Before leaving the science museum, Caleb found a really cool computer game all about metrics. Caleb had been practicing his metric conversions while playing at the Metric Playground, but now it was time for him to apply what he had learned.
The object of the game is to move the mountain climber up the mountain by solving problems involving metric lengths, weights and liquids. Each time a correct answer is given, the mountain climber moves up the mountain. You keep playing until the climber reaches the top.
At the beginning of the game, Caleb sees this problem on the computer screen. It is a problem that requires Caleb to use greater than or less than symbols to compare two values.
5.5 grams _____ 4500 mg
Caleb is unsure of the correct answer. He decides to skip this problem by pushing the NEXT button on the computer.
Here is Caleb’s second problem.
6.7 Liters x 10 = _____
Caleb thought that the answer was 6700 so he entered that answer into the computer.
TRY AGAIN popped up on his screen.
Finally Caleb decided to try one more problem.
______ kilograms is one hundred times lighter than 1550 kilograms
Caleb is stuck again.
We are going to help Caleb answer all three questions. Let’s start with the first one.
5.5 grams _____ 4500 mg
There are 1000 mg in 1 gram. Therefore, if we change the 4500 milligrams to grams by moving the decimal point three places to the left, we end up with 4.5 grams. 5.5 is greater than 4.5.
5.5 grams > 4500 mg
The second problem requires multiplying by powers of ten.
6.7 liters \begin{align*}\times\end{align*} 10 \begin{align*}=\end{align*} _____
To multiply by a power of ten we move the decimal point to the right. Here we are multiplying by 10, so we move the decimal point one place to the right.
6.7 liters \begin{align*}\times\end{align*} 10 \begin{align*}=\end{align*} 67 liters
Our final problem involves division by powers of ten.
______ kilograms is one hundred times lighter than 1550 kilograms
We want to make 1550 kg 100 times lighter. To do this, we divide by 100. To divide by 100, a power of 10, we move the decimal point two places to the left.
15.5 kg is our answer.
Technology Integration
James Sousa Metric Unit Conversion
Other Videos:
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/6_Weight_and_Capacity/index.html – A great video on weight and capacity using metric and customary units
Time to Practice
Directions: Compare the following metric units using >, <, or =.
1. 5 cm ______ 60 mm
2. 105 mm ______ 10 cm
3. 6000 mg ______ 6 kg
4. 7.8 L ______ 780 mL
5. 65 L ______ 65000 mL
6. 102 cm ______ 1000 mm
Directions: Convert each measurement using powers of ten.
7. 5.6 km = ______ m
8. 890 m = ______ km
9. 9230 m = ______ km
10. 40 cm = ______ mm
11. 5000 mm = ______ cm
12. 500 cm = ______ m
13. 7.9 m = ______ cm
14. 99 m = ______ cm
15. 460 cm = ______ m
16. 34 cm = ______ m
17. 4.3 km = ______ m
18. 760 m = ______ km
19. 4300 m = ______ km
20. 5000 g = ______ kg
21. 560 mL = ______ L
22. 6210 mL = ______ L
23. 8900 mL = ______ L
24. 7.5 L = ______ mL
25. .5 L = ______ mL
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