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Kari’s newborn baby weighed 2,800 grams. How many kilograms did the baby weigh?

2.8 kilograms

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Anderson received a package that was marked 4,500 grams. How many kilograms did this package weigh?

4.5 kilograms

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As you become familiar with the metric system you may see a pattern. Since the system is based on multiples of ten, the calculations involve multiplying by multiples of ten. We have learned how to simplify these calculations by just moving the decimal.

To multiply by 10, 100, or 1,000, we move the decimal to the right one, two, or three places, respectively. To multiply by 0.1, 0.01, or 0.001, we move the decimal to the left one, two, or three places, respectively.

We can apply this pattern when we make measurement conversions in the metric system. In [link] , we changed 3,200 grams to kilograms by multiplying by 1 1000 (or 0.001). This is the same as moving the decimal three places to the left.

We have the statement 3200 g times the fraction 1 kg over 1000 g, with the g’s crossed out. Below this, we have 3.2. We also have the statement 3200 times 1/1000, with an arrow drawn from the right of the final 0 in 3200 to the space between the 0’s, to the space between the 2 and the 0, and then to the space between the 3 and the 2. Below this, we have 3.2.

Convert 350 L to kiloliters 4.1 L to milliliters.

Solution

  1. We will convert liters to kiloliters. In [link] , we see that 1 kiloliter = 1,000 liters.
    350 L
    Multiply by 1, writing 1 as a fraction relating liters to kiloliters. 350 L 1 kL 1,000 L
    Simplify. 350 L 1 kL 1,000 L
    . 0.35 kL


  2. We will convert liters to milliliters. From [link] we see that 1 liter = 1,000 milliliters.
    .
    Multiply by 1, writing 1 as a fraction relating liters to milliliters. .
    Simplify. .
    Move the decimal 3 units to the right. .
    .
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Convert: 725 L to kiloliters 6.3 L to milliliters

7,250 kiloliters 6,300 milliliters

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Convert: 350 hL to liters 4.1 L to centiliters

35,000 liters 410 centiliters

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Use mixed units of measurement in the metric system

Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the US system. But it may be easier because of the relation of the units to the powers of 10. Make sure to add or subtract like units.

Ryland is 1.6 meters tall. His younger brother is 85 centimeters tall. How much taller is Ryland than his younger brother?

Solution

We can convert both measurements to either centimeters or meters. Since meters is the larger unit, we will subtract the lengths in meters. We convert 85 centimeters to meters by moving the decimal 2 places to the left.

Write the 85 centimeters as meters. 1.60 m −0.85 m _______ 0.75 m

Ryland is 0.75 m taller than his brother.

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Mariella is 1.58 meters tall. Her daughter is 75 centimeters tall. How much taller is Mariella than her daughter? Write the answer in centimeters.

83 centimeters

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The fence around Hank’s yard is 2 meters high. Hank is 96 centimeters tall. How much shorter than the fence is Hank? Write the answer in meters.

1.04 meters

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Dena’s recipe for lentil soup calls for 150 milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?

Solution

We will find the amount of olive oil in millileters then convert to liters.

Triple 150 mL Translate to algebra. 3 · 150 mL Multiply. 450 mL Convert to liters. 450 · 0.001 L 1 mL Simplify. 0.45 L Dena needs 0.45 liters of olive oil.

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A recipe for Alfredo sauce calls for 250 milliliters of milk. Renata is making pasta with Alfredo sauce for a big party and needs to multiply the recipe amounts by 8. How many liters of milk will she need?

2 liters

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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