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Have you ever run a or race? The lengths of those races are measured in kilometers. The metric system is commonly used in the United States when talking about the length of a race.
Nick ran a race. How many meters did he run?
We will convert kilometers to meters using the Identity Property of Multiplication and the equivalencies in
[link] .
| 10 kilometers | |
| Multiply the measurement to be converted by 1. |
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| Write 1 as a fraction relating kilometers and meters. |
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| Simplify. |
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| Multiply. | 10,000 m |
| Nick ran 10,000 meters. |
Sandy completed her first race. How many meters did she run?
5000 m
Herman bought a rug meters in length. How many centimeters is the length?
250 cm
Eleanor’s newborn baby weighed grams. How many kilograms did the baby weigh?
We will convert grams to kilograms.
 | |
| Multiply the measurement to be converted by 1. |
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| Write 1 as a fraction relating kilograms and grams. |
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| Simplify. |
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| Multiply. |
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| Divide. | 3.2 kilograms |
| The baby weighed kilograms. |
Kari’s newborn baby weighed grams. How many kilograms did the baby weigh?
2.8 kilograms
Anderson received a package that was marked grams. How many kilograms did this package weigh?
4.5 kilograms
Since the metric system is based on multiples of ten, conversions involve multiplying by multiples of ten. In Decimal Operations , we learned how to simplify these calculations by just moving the decimal.
To multiply by we move the decimal to the right places, respectively. To multiply by we move the decimal to the left places respectively.
We can apply this pattern when we make measurement conversions in the metric system.
In [link] , we changed grams to kilograms by multiplying by This is the same as moving the decimal places to the left.
Convert: ⓐ liters to kiloliters ⓑ liters to milliliters.
ⓐ We will convert liters to kiloliters. In
[link] , we see that
| 350 L | |
| Multiply by 1, writing 1 as a fraction relating liters to kiloliters. |
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| Simplify. |
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| Move the decimal 3 units to the left. |
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| 0.35 kL |
ⓑ We will convert liters to milliliters. In
[link] , we see that
| 4.1 L | |
| Multiply by 1, writing 1 as a fraction relating milliliters to liters. |
 |
| Simplify. |
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| Move the decimal 3 units to the left. |
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| 4100 mL |
Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system . But it may be easier because of the relation of the units to the powers of We still must make sure to add or subtract like units.
Ryland is meters tall. His younger brother is centimeters tall. How much taller is Ryland than his younger brother?
We will subtract the lengths in meters. Convert centimeters to meters by moving the decimal places to the left; cm is the same as m.
Now that both measurements are in meters, subtract to find out how much taller Ryland is than his brother.
Ryland is meters taller than his brother.
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