2.23: Estimation of Conversion to Metric Units
Have you ever gotten a new camera? Well, Marc received one before his big trip to Boston.
Before going to Boston for the month, Marc was given a new camera for the trip. The new camera has a 55 mm lens. Marc enjoyed reading all about his new camera and spent time trying it out. He wondered what the measurement of the lens would be in inches if it is 55 mm in metrics.
Do you know?
This Concept will teach you how to estimate equivalence between metric and customary units of measure. Then we'll come back to this dilemma at the end of the Concept.
Guidance
We have been working inside the metric system of measurement.
Did you know there is another system of measurement? The customary system of measurement is widely-used in the United States. You are probably already familiar with some of the customary units. Customary units of length include the inch, foot, yard, and mile; for weight, ounce and pound; for capacity, teaspoon, cup, pint, quart, and gallon.
We encounter both metric units and customary units all the time—sometimes at the same time. One important aspect to understanding measurement is developing a general idea of the equivalence between the two systems.
The chart below shows the estimated metric equivalent to common customary units. Notice how all the customary units are in units of 1. 1 foot, for instance, is about 30.48 centimeters, so 2 feet is about 60.96 centimeters or \begin{align*}30.48 \times 2\end{align*}. If you had a measurement in centimeters and wanted to estimate the number of inches, you would reverse the process, or divide by 30.48.
Customary Units | Metric Units |
---|---|
1 inch | 25.4 millimeters |
1 foot | 30.48 centimeters |
1 yard | 0.91 meters |
1 mile | 1.61 kilometers |
1 teaspoon | 4.93 milliliters |
1 cup | 0.24 liters |
1 pint | 0.47 liters |
1 quart | 0.95 liters |
1 gallon | 3.79 liters |
1 ounce | 28.35 grams |
1 pound | 0.45 kilograms |
Completing these calculations exactly can be very tricky, so we use estimation to determine equivalence.
How many cups are equal to .48 liters?
To answer this question, we can look at the chart. We can see that one cup is equal to .47 liters. Therefore, we can say that 2 cups is equal to .48 liters.
Our answer is 2 cups.
4 kilograms is equal to how many pounds?
First, let’s look at the number of pounds to kilograms on our chart. 1 pound is equal to a little less than one-half of a kilogram. To find the number of pounds in a one kilogram, we can multiply the pounds by 2. 2 pounds are in 1 kilogram. Therefore, there are 8 pounds in four kilograms.
By estimating, we can find approximate equivalent measures for customary and metric units of measure!!
Metric units play key roles in measurements of sports figures—in track and field distances like the one in our introduction problem, in the size of an Olympic swimming pool, in the length and width of football fields and basketball courts. But metric units play important roles in many other aspects of everyday life—from the weight of vegetables at the farmer’s market, to the width of the living room drapes.
Now that you know how to convert and compare across metric units, you can use this knowledge to examine different situations.
Example A
4 gallons = _____ liters
Solution: Between 15 - 16 liters
Example B
60 cm = _____feet
Solution: About 2 feet
Example C
3 cups = _____ liters
Solution: About .75 liters
Here is the original problem once again.
Before going to Boston for the month, Marc was given a new camera for the trip. The new camera has a 55 mm lens. Marc enjoyed reading all about his new camera and spent time trying it out. He wondered what the measurement of the lens would be in inches if it is 55 mm in metrics.
Do you know?
To figure this out, first think about the chart of equivalent measures that was presented earlier in this Concept.
Customary Units | Metric Units |
---|---|
1 inch | 25.4 millimeters |
1 foot | 30.48 centimeters |
1 yard | 0.91 meters |
1 mile | 1.61 kilometers |
1 teaspoon | 4.93 milliliters |
1 cup | 0.24 liters |
1 pint | 0.47 liters |
1 quart | 0.95 liters |
1 gallon | 3.79 liters |
1 ounce | 28.35 grams |
1 pound | 0.45 kilograms |
If one inch equals 25.4 mm, then how many inches does 55 millimeters represent?
We can use mental math to figure this out.
55 mm is a little more than 2(25.4).
We can say then that 55 mm is about two inches. This is our answer.
Vocabulary
Here are the vocabulary words in this Concept.
- Metric System
- a system of measurement developed by the French. Some units include meters, grams and liters.
- Customary System
- a system of measurement common in the United States. Some units include feet, pounds and gallons.
- Estimate
- to find an approximate measurement, useful in figuring out a reasonable number and not an exact one.
- Equivalence
- means equal.
Guided Practice
Here is one for you to try on your own.
At the Harvest Festival, Jocelyn is trying to buy the largest pumpkin. Covert the mass of the following pumpkins into the same unit and order the pumpkins from greatest to least.
Pumpkin J—5.67 kg
Pumpkin K—5,510,000 mg
Pumpkin L—567,100 cg
Pumpkin M—5,800 g
Answer
This problem asks us to order the pumpkins from greatest to least mass. In order to do so, we need to get all of the pumpkins into the same units. We’ll covert them to grams because grams is a good middle-point between the units.
- Pumpkin J has a mass of 5.67 kg. To convert to grams, we need to multiply by 1,000 or move the decimal point three places to the right. 5.67 kg \begin{align*}\rightarrow\end{align*} 5,670 grams.
- Pumpkin K has a mass of 5,510,000 mg. To convert to grams, we need to divide by 1,000 or move the decimal point three places to the left. 5,510,000 mg \begin{align*}\rightarrow\end{align*} 5,510 grams.
- Pumpkin L has a mass of 567,100 cg. To convert to grams, we need to divide by 100 or move the decimal point two places to the left. 567,100 cg \begin{align*}\rightarrow\end{align*} 5,671 grams.
- Pumpkin M is already in grams \begin{align*}\rightarrow\end{align*} 5,800 grams.
The answer is Pumpkin M, Pumpkin L, Pumpkin J, Pumpkin K.
Video Review
Here is a video for review.
http://www.youtube.com/watch?v=y2RHWA70WM - This is a Khan Academy Video on customary and metric units of measurement.
Practice
Directions: Estimate a metric equivalent for the following customary measurements.
1. 5 cups to liters
2. 5 yards to meters
3. 6 inches to mm
4. 15 pounds to kg
5. 1 cup to liters
6. 4 miles to km
7. 5 feet to cm
8. 12 feet to cm
9. 8 inches to mm
10. 28.5 ounces to grams
11. 11.75 inches to millimeters
12. 8 quarts to liters
13. 15 pounds to kilograms
Directions: Solve the following problems.
14. To join the swim team, Jessica swam every day. The distances she swam for the first four days were as follows: 1.65 km, 1,750 m, 185,000 cm, 1,950,000 mm. If the pattern continues, how many kilometers will she swim on the fifth day?
15. Mrs. Roth is moving to a new apartment. She can lift exactly 22.5 kg. Which of the following objects can she lift: box of books (23,500 g), statue (2,450,000 cg), computer (2,550,000 mg), potted plant (22.55 kg)?
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Image Attributions
Here you'll learn to estimate equivalence between metric and customary units of measure.