Convert 16,848 dm³ to Liters: Volume Unit Conversion Problem

Q: Why is 1 dm³ exactly equal to 1 liter?

This is by definition! A liter was originally defined as the volume of 1 cubic decimeter. Since 1 decimeter = 10 cm, a cubic decimeter contains $ 10 \times 10 \times 10 = 1000 \, \text{cm}^3 $, which equals 1 liter.

Q: Do I need to multiply or divide by anything?

No calculation needed! Since $ 1 \, \text{dm}^3 = 1 \, \text{l} $, you simply keep the same number. $ 16,848 \, \text{dm}^3 $ becomes $ 16,848 \, \text{l} $.

Q: What if I accidentally used cubic centimeters instead?

If you confused cubic centimeters with cubic decimeters, you'd divide by 1000 (since $ 1000 \, \text{cm}^3 = 1 \, \text{l} $). But the problem clearly states dm³, so no division needed!

Q: How can I remember this conversion?

Think of it as "decimeter cubed = liter". Both are common metric units for volume, and they were designed to have this simple 1:1 relationship to make conversions easy!

Q: What about other volume unit conversions?

Other conversions need calculations: $ 1 \, \text{m}^3 = 1000 \, \text{l} $ and $ 1000 \, \text{cm}^3 = 1 \, \text{l} $. But dm³ to liters is always 1:1 - the simplest conversion!

Volume Conversion with Cubic Decimeters

Convert $16,848dm^3$ into liters.

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Understand the problem

Convert $16,848dm^3$ into liters.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the conversion

Now, let's work through each step:
Step 1: The problem provides us with the volume $16,848 \, \text{dm}^3$ .
Step 2: We know that $1 \, \text{dm}^3 = 1 \, \text{l}$ . This means that each cubic decimeter is equivalent to one liter.
Step 3: Using this direct equivalence, we can convert $16,848 \, \text{dm}^3$ directly into $16,848 \, \text{l}$ .

Therefore, the volume of $16,848 \, \text{dm}^3$ is equivalent to $16,848 \, \text{l}$ .

Final Answer

$16,848l$

Key Points to Remember

Essential concepts to master this topic

Rule: One cubic decimeter equals exactly one liter always
Technique: Direct conversion means $16,848 \, \text{dm}^3 = 16,848 \, \text{l}$
Check: Verify using definition: 1 dm = 10 cm cube gives 1000 cm³ = 1 liter ✓

Common Mistakes

Avoid these frequent errors

Dividing by 10, 100, or 1000 when converting dm³ to liters
Don't divide 16,848 by 1000 to get 16.848 liters = wrong answer! This confuses cubic decimeters with cubic centimeters or other units. Always remember that cubic decimeters and liters have a direct 1:1 relationship.

Practice Quiz

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How many cm³ are there in a m³?

FAQ

Everything you need to know about this question

Why is 1 dm³ exactly equal to 1 liter?

This is by definition! A liter was originally defined as the volume of 1 cubic decimeter. Since 1 decimeter = 10 cm, a cubic decimeter contains $10 \times 10 \times 10 = 1000 \, \text{cm}^3$ , which equals 1 liter.

Do I need to multiply or divide by anything?

No calculation needed! Since $1 \, \text{dm}^3 = 1 \, \text{l}$ , you simply keep the same number. $16,848 \, \text{dm}^3$ becomes $16,848 \, \text{l}$ .

What if I accidentally used cubic centimeters instead?

If you confused cubic centimeters with cubic decimeters, you'd divide by 1000 (since $1000 \, \text{cm}^3 = 1 \, \text{l}$ ). But the problem clearly states dm³, so no division needed!

How can I remember this conversion?

Think of it as "decimeter cubed = liter". Both are common metric units for volume, and they were designed to have this simple 1:1 relationship to make conversions easy!

What about other volume unit conversions?

Other conversions need calculations: $1 \, \text{m}^3 = 1000 \, \text{l}$ and $1000 \, \text{cm}^3 = 1 \, \text{l}$ . But dm³ to liters is always 1:1 - the simplest conversion!

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