Convert 2 3/6 m³ to Cubic Decimeters: Volume Unit Conversion

Q: Why do I need to convert the mixed number first?

Mixed numbers like $ 2\frac{3}{6} $ are harder to multiply! Converting to 2.5 makes the calculation much easier: 2.5 × 1000 = 2500.

Q: How do I remember the conversion from m³ to dm³?

Think about it step by step: 1 meter = 10 decimeters. For volume, you need length × width × height, so it's 10 × 10 × 10 = 1000. Therefore, 1 m³ = 1000 dm³.

Q: Why is the answer so much bigger than the original number?

That's normal! When converting to smaller units, you get more of them. A cubic decimeter is much smaller than a cubic meter, so you need 1000 dm³ to equal just 1 m³.

Q: What if I forgot to simplify 3/6 first?

You can still solve it! $ 2\frac{3}{6} = 2 + \frac{3}{6} = 2 + 0.5 = 2.5 $. But it's easier to simplify fractions first: $ \frac{3}{6} = \frac{1}{2} = 0.5 $.

Q: How can I check if 2500 dm³ is reasonable?

Use estimation! $ 2\frac{1}{2} $ is about 2.5 m³. Since 1 m³ = 1000 dm³, then 2.5 × 1000 = 2500 dm³. The answer makes sense!

Volume Unit Conversion with Mixed Numbers

Convert $2\frac{3}{6}m^3$ into cubic decimeters.

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Understand the problem

Convert $2\frac{3}{6}m^3$ into cubic decimeters.

Step-by-step solution

To solve this problem, we need to convert the volume $2\frac{3}{6} \, m^3$ to cubic decimeters.

Step 1: Convert the fractional volume to a decimal. $2\frac{3}{6} \, m^3 = 2.5 \, m^3$ .
Step 2: Use the conversion factor $1 \, m^3 = 1000 \, dm^3$ .
Step 3: Multiply 2.5 by 1000 to change the unit from cubic meters to cubic decimeters.

Calculation:

$2.5 \, m^3 \times 1000 \, dm^3/m^3 = 2500 \, dm^3$

Therefore, the volume of $2\frac{3}{6} \, m^3$ is equivalent to $\mathbf{2500 \, dm^3}$ .

Final Answer

$2500dm^3$

Key Points to Remember

Essential concepts to master this topic

Mixed Numbers: Convert $2\frac{3}{6}$ to decimal first: 2.5
Conversion Factor: Use $1 m^3 = 1000 dm^3$ to multiply 2.5 × 1000
Check: Verify units changed correctly: $m^3$ becomes $dm^3$ with larger number ✓

Common Mistakes

Avoid these frequent errors

Using wrong conversion factor for cubic units
Don't use 1 m = 10 dm for cubic conversions = gives 25 dm³ instead of 2500 dm³! This ignores that cubic units need the linear conversion cubed (10³ = 1000). Always remember: 1 m³ = 1000 dm³ for volume conversions.

Practice Quiz

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How many cm³ are there in a m³?

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number first?

Mixed numbers like $2\frac{3}{6}$ are harder to multiply! Converting to 2.5 makes the calculation much easier: 2.5 × 1000 = 2500.

How do I remember the conversion from m³ to dm³?

Think about it step by step: 1 meter = 10 decimeters. For volume, you need length × width × height, so it's 10 × 10 × 10 = 1000. Therefore, 1 m³ = 1000 dm³.

Why is the answer so much bigger than the original number?

That's normal! When converting to smaller units, you get more of them. A cubic decimeter is much smaller than a cubic meter, so you need 1000 dm³ to equal just 1 m³.

What if I forgot to simplify 3/6 first?

You can still solve it! $2\frac{3}{6} = 2 + \frac{3}{6} = 2 + 0.5 = 2.5$ . But it's easier to simplify fractions first: $\frac{3}{6} = \frac{1}{2} = 0.5$ .

How can I check if 2500 dm³ is reasonable?

Use estimation! $2\frac{1}{2}$ is about 2.5 m³. Since 1 m³ = 1000 dm³, then 2.5 × 1000 = 2500 dm³. The answer makes sense!

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