Converting Metric Volume Units

In the lesson on metric volume units you learned that $1$ L $= 1000$ mL. Between the liter and the milliliter there are two more units, and above the liter there are bigger ones. Together they form the **metric capacity ladder**: $$\text{kL} \xrightarrow{\times 10} \text{hL} \xrightarrow{\times 10} \text{daL} \xrightarrow{\times 10} \text{L} \xrightarrow{\times 10} \text{dL} \xrightarrow{\times 10} \text{cL} \xrightarrow{\times 10} \text{mL}$$ Each step on the ladder is a factor of $10$ (the decaliter, daL, is rarely used, but it keeps the steps even): - $1$ L $= 10$ dL $= 100$ cL $= 1000$ mL - $1$ hL $= 100$ L and $1$ kL $= 1000$ L **How to convert:** - From a **bigger** unit to a **smaller** unit: **multiply** (the number gets bigger) - From a **smaller** unit to a **bigger** unit: **divide** (the number gets smaller) - Count the steps: $1$ step $= 10$, $2$ steps $= 100$, $3$ steps $= 1000$ **Capacity and cubic units are linked:** $$1 \text{ mL} = 1 \text{ cm}^3 \qquad 1 \text{ L} = 1 \text{ dm}^3 = 1000 \text{ cm}^3 \qquad 1 \text{ m}^3 = 1000 \text{ L}$$

Liters to Centiliters

A bottle of juice holds $3.5$ L. How many centiliters is that?

Find the direction: L is bigger than cL, so we go down the ladder = Multiply

Count the steps: L $\to$ dL $\to$ cL is $2$ steps = Factor $100$

Calculate: $3.5 \times 100 = 350$ = $350$ cL

Answer: $3.5$ L $= 350$ cL

Deciliters to Milliliters

A recipe asks for $2.4$ dL of milk. Your measuring jug shows milliliters. How many mL do you pour?

Find the direction: dL is bigger than mL = Multiply

Count the steps: dL $\to$ cL $\to$ mL is $2$ steps = Factor $100$

Calculate: $2.4 \times 100 = 240$ = $240$ mL

Answer: $2.4$ dL $= 240$ mL

From Cubic Centimeters to Liters

An aquarium is $50$ cm long, $30$ cm wide and $20$ cm high. How many liters of water does it hold when full?

Find the volume in cm³: $50 \times 30 \times 20 = 30\,000$ = $30\,000$ cm³

Use $1$ cm³ $= 1$ mL: $30\,000$ cm³ $= 30\,000$ mL = $30\,000$ mL

Convert mL to L: $30\,000 \div 1000 = 30$ = $30$ L

Answer: The aquarium holds $30$ L of water.

Comparing Amounts in Different Units

Order from smallest to largest: $0.6$ L, $58$ cL, $590$ mL, $6.2$ dL.

Choose one unit: Convert everything to mL (the smallest unit, so no decimals) = Common unit: mL

Convert each amount: $0.6 \times 1000 = 600$, $58 \times 10 = 580$, $590$, $6.2 \times 100 = 620$ = $600$, $580$, $590$, $620$ mL

Order the numbers: $580 < 590 < 600 < 620$ = Smallest to largest

Write the original amounts: $58$ cL, $590$ mL, $0.6$ L, $6.2$ dL = Done

Answer: $58$ cL $< 590$ mL $< 0.6$ L $< 6.2$ dL

A Multi-Step Problem with Cubic Meters

A water tank holds $1.5$ m³. How many $12$ L watering cans can you fill from the full tank?

Convert m³ to liters: $1$ m³ $= 1000$ L, so $1.5 \times 1000 = 1500$ = $1500$ L

Both amounts are now in liters: Tank: $1500$ L, can: $12$ L = Same unit

Divide: $1500 \div 12 = 125$ = $125$ cans

Answer: You can fill $125$ watering cans.

Metric volume units appear in many forms, and you often need to switch between them: - **Shopping**: A can holds $33$ cL, a bottle holds $1.5$ L. Which is more? Only a conversion tells you. - **Cooking**: Many European recipes use deciliters ($2$ dL of milk) while a measuring jug shows milliliters. - **Aquariums and pools**: You measure a tank in centimeters or meters, but the water is sold and pumped in liters. - **Water bills**: Water companies charge per cubic meter, and $1$ m³ is $1000$ L. - **Science**: Lab cylinders show mL, and $1$ mL is exactly $1$ cm³. Once you know the ladder, every metric volume conversion is just multiplying or dividing by $10$, $100$ or $1000$.

Mistake: Using $1000$ for every conversion, for example writing $2$ L $= 2000$ cL

Why: Only L to mL is $3$ steps. L to cL is just $2$ steps on the ladder.

Correct: Count the steps: L $\to$ dL $\to$ cL is $2$ steps, so multiply by $100$: $2$ L $= 200$ cL.

Mistake: Multiplying when going to a bigger unit, for example $40$ cL $= 400$ L

Why: A liter is much bigger than a centiliter, so you need fewer liters than centiliters.

Correct: Smaller to bigger unit: divide. $40 \div 100 = 0.4$, so $40$ cL $= 0.4$ L.

Mistake: Comparing the numbers without converting: thinking $58$ cL is more than $0.6$ L because $58 > 0.6$

Why: The numbers are in different units, so they cannot be compared directly.

Correct: Convert first: $58$ cL $= 580$ mL and $0.6$ L $= 600$ mL, so $0.6$ L is more.

Mistake: Forgetting the placeholder zero: writing $85$ mL $= 0.85$ L

Why: Dividing by $1000$ moves the decimal point $3$ places, and $85$ has only $2$ digits.

Correct: Fill the empty place with a zero: $85 \div 1000 = 0.085$, so $85$ mL $= 0.085$ L.

Cooking with Mixed Units

European recipes often mix deciliters, centiliters and milliliters, so cooks convert everything to one unit before measuring.

A pancake recipe needs $2.5$ dL of milk. On a jug marked in mL, that is $250$ mL.

Filling an Aquarium

Pet shops measure tanks in centimeters, but water treatment and fish numbers depend on liters. Because $1000$ cm³ $= 1$ L, the conversion is quick.

A small tank of $30$ cm $\times$ $20$ cm $\times$ $25$ cm holds $15\,000$ cm³, which is $15$ L.

Water Delivery

Water trucks are filled in kiloliters, while tanks at homes and farms are often sold by their size in cubic meters.

A truck with $10$ kL of water carries $10\,000$ L, which is also $10$ m³.

The capacity ladder is kL, hL, daL, L, dL, cL, mL, and each step is a factor of $10$

$1$ L $= 10$ dL $= 100$ cL $= 1000$ mL; $1$ hL $= 100$ L; $1$ kL $= 1000$ L

Bigger unit to smaller unit: multiply. Smaller unit to bigger unit: divide

$1$ mL $= 1$ cm³, $1$ L $= 1$ dm³ $= 1000$ cm³ and $1$ m³ $= 1000$ L

To compare amounts, convert them all to the same unit first

When dividing, fill empty places with zeros: $85$ mL $= 0.085$ L

Q: How do I know whether to multiply or divide?

A: Ask yourself which unit is bigger. Going to a smaller unit means you need more of them, so multiply. Going to a bigger unit means you need fewer of them, so divide.

Q: Is $1$ mL really the same as $1$ cm³?

A: Yes. A cube that is $1$ cm on each side holds exactly $1$ mL. That is why a $10$ cm cube ($1000$ cm³) holds exactly $1$ L.

Q: Why do I almost never see decaliters?

A: The decaliter ($10$ L) is a correct metric unit but rarely used in daily life. It is still useful on the ladder, because it keeps every step equal to $10$.

Q: Where do I see centiliters and deciliters?

A: On drink cans and bottles in many countries ($33$ cL, $50$ cL) and in recipes ($2$ dL of cream). Measuring jugs usually show mL, so you convert.

Exit Presentation

Converting Metric Volume Units

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Measurement / Volume & Capacity

Converting Metric Volume Units

Convert between liters, deciliters, centiliters and milliliters, and link them to cubic centimeters and cubic meters.

Elementary25 min

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