Convert 61½ Cubic Centimeters to Cubic Decimeters: Step-by-Step Volume Conversion

Q: Why do I divide by 1000 instead of 100?

Because we're dealing with cubic units, not linear units! Since 1 dm = 10 cm, then $ 1 \text{ dm}^3 = 10^3 = 1000 \text{ cm}^3 $. The exponent makes all the difference!

Q: How do I convert the mixed number 61½?

Convert to decimal: $ 61\frac{1}{2} = 61 + 0.5 = 61.5 $. Or keep as fraction: $ \frac{123}{2} $. Both work perfectly for the division!

Q: Should my answer be a decimal or fraction?

Either form is correct! $ 0.0615 \text{ dm}^3 $ and $ \frac{61.5}{1000} \text{ dm}^3 $ are the same value. Choose the form that matches the answer choices given.

Q: How can I remember which direction to convert?

Remember: smaller units to larger units = divide. Since cm³ are smaller than dm³, you divide. Think of it like having 1000 pennies = 10 dollars (divide by 100).

Q: What if I get confused about the units?

Draw a cube! A 1 dm × 1 dm × 1 dm cube contains 10 cm × 10 cm × 10 cm = 1000 small cubes. This visual helps you remember the 1000 relationship.

Volume Conversion with Mixed Numbers

Convert $61\frac{1}{2}cm^3$ into cubic decimeter.

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Understand the problem

Convert $61\frac{1}{2}cm^3$ into cubic decimeter.

Step-by-step solution

Let's solve the problem through a series of steps for ease of understanding:

Step 1: Identify the volume in cubic centimeters.
The given volume is $61\frac{1}{2} \, \text{cm}^3$ .
Step 2: Convert the mixed number to an improper fraction.
The mixed number $61\frac{1}{2}$ can be rewritten as $61 + \frac{1}{2}$ which equals $\frac{122}{2} + \frac{1}{2} = \frac{123}{2}$ . This is equivalent to 61.5 cubic centimeters.
Step 3: Convert cubic centimeters to cubic decimeters.
Using the fact that $1 \, \text{dm}^3 = 1000 \, \text{cm}^3$ , we divide the given volume by 1000 to convert from cubic centimeters to cubic decimeters.
$\frac{123}{2} \div 1000 = \frac{123}{2000} = \frac{61.5}{1000}$

Therefore, the volume in cubic decimeters is $\frac{61.5}{1000} \, \text{dm}^3$ .

Upon examining the available choices, choice 1: $\frac{61.5}{1000 \, \text{dm}^3}$ is the correct answer.

The solution to the problem is $\frac{61.5}{1000 \, \text{dm}^3}$ .

Final Answer

$\frac{61.5}{1000dm^3}$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: 1 cubic decimeter equals 1000 cubic centimeters
Technique: Convert $61\frac{1}{2}$ to 61.5, then divide by 1000
Check: $\frac{61.5}{1000} \times 1000 = 61.5 \text{ cm}^3$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying by 1000 instead of dividing
Don't multiply 61.5 by 1000 = 61,500 dm³! This makes the volume impossibly large because you're going from smaller units to larger units. Always divide by 1000 when converting cm³ to dm³.

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 divide by 1000 instead of 100?

Because we're dealing with cubic units, not linear units! Since 1 dm = 10 cm, then $1 \text{ dm}^3 = 10^3 = 1000 \text{ cm}^3$ . The exponent makes all the difference!

How do I convert the mixed number 61½?

Convert to decimal: $61\frac{1}{2} = 61 + 0.5 = 61.5$ . Or keep as fraction: $\frac{123}{2}$ . Both work perfectly for the division!

Should my answer be a decimal or fraction?

Either form is correct! $0.0615 \text{ dm}^3$ and $\frac{61.5}{1000} \text{ dm}^3$ are the same value. Choose the form that matches the answer choices given.

How can I remember which direction to convert?

Remember: smaller units to larger units = divide. Since cm³ are smaller than dm³, you divide. Think of it like having 1000 pennies = 10 dollars (divide by 100).

What if I get confused about the units?

Draw a cube! A 1 dm × 1 dm × 1 dm cube contains 10 cm × 10 cm × 10 cm = 1000 small cubes. This visual helps you remember the 1000 relationship.

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