Order Measurements: Converting mm, cm, m, and dm to Compare Lengths

Q: Which unit should I convert everything to?

Choose the smallest unit in your list (usually mm for length). This avoids decimals and makes comparison easier. For example, convert to mm rather than m to work with whole numbers.

Q: How do I remember the conversion factors?

Use the pattern: mm → cm → dm → m. Each step multiplies by 10: 1 cm = 10 mm, 1 dm = 10 cm = 100 mm, 1 m = 10 dm = 1000 mm.

Q: What if I get confused with the decimal conversions?

Focus on whole number conversions first. For 0.09 dm: multiply 0.09 × 100 mm = 9 mm. Breaking it into steps: 0.09 dm → 0.9 cm → 9 mm makes it clearer.

Q: Can I convert to a different unit like cm instead?

Absolutely! You could convert everything to cm: 60 mm = 6 cm, 0.09 dm = 0.9 cm, 0.1 m = 10 cm. The final order will be the same regardless of which unit you choose.

Unit Conversion with Mixed Metric Units

Order from smallest to largest:

$60$ mm, $8$ cm, $0.1$ m, $0.09$ dm

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Order from smallest to largest:

$60$ mm, $8$ cm, $0.1$ m, $0.09$ dm

Step-by-step solution

To solve this problem, we'll convert each measurement to millimeters and order them accordingly.

Step-by-step solution:

Convert each measurement to millimeters:

$60$ mm is already in millimeters.
$8$ cm: Since $1$ cm equals $10$ mm, $8$ cm is $8 \times 10 = 80$ mm.
$0.1$ m: Since $1$ m equals $1000$ mm, $0.1$ m is $0.1 \times 1000 = 100$ mm.
$0.09$ dm: Since $1$ dm equals $100$ mm and $0.09$ dm equals $0.09 \times 100 = 9$ mm.

List the lengths in millimeters: $9$ mm (from $0.09$ dm), $60$ mm, $80$ mm (from $8$ cm), $100$ mm (from $0.1$ m).
Order the original measurements from smallest to largest:

$0.09$ dm
$60$ mm
$8$ cm
$0.1$ m

Therefore, the solution to the problem is:

$0.09$ dm
$60$ mm
$8$ cm
$0.1$ m

Final Answer

$0.09$ dm
$60$ mm
$8$ cm
$0.1$ m

Key Points to Remember

Essential concepts to master this topic

Conversion: Convert all measurements to same unit before comparing
Technique: Use mm as base: 8 cm = 8 × 10 = 80 mm
Check: Verify order: 9 mm < 60 mm < 80 mm < 100 mm ✓

Common Mistakes

Avoid these frequent errors

Comparing numbers without converting units first
Don't compare 60 mm with 8 cm directly thinking 60 > 8 = wrong order! Different units make direct comparison impossible and lead to incorrect rankings. Always convert all measurements to the same unit before ordering.

Practice Quiz

Test your knowledge with interactive questions

Convert to meters:
$$ 40 $$ cm

FAQ

Everything you need to know about this question

Which unit should I convert everything to?

Choose the smallest unit in your list (usually mm for length). This avoids decimals and makes comparison easier. For example, convert to mm rather than m to work with whole numbers.

How do I remember the conversion factors?

Use the pattern: mm → cm → dm → m. Each step multiplies by 10: 1 cm = 10 mm, 1 dm = 10 cm = 100 mm, 1 m = 10 dm = 1000 mm.

What if I get confused with the decimal conversions?

Focus on whole number conversions first. For 0.09 dm: multiply 0.09 × 100 mm = 9 mm. Breaking it into steps: 0.09 dm → 0.9 cm → 9 mm makes it clearer.

Can I convert to a different unit like cm instead?

Absolutely! You could convert everything to cm: 60 mm = 6 cm, 0.09 dm = 0.9 cm, 0.1 m = 10 cm. The final order will be the same regardless of which unit you choose.

How do I check if my final order is correct?

Convert everything to the same unit and list the numbers: 9, 60, 80, 100. These should be in ascending order. Then match each number back to its original measurement.

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Order Measurements: Converting mm, cm, m, and dm to Compare Lengths

Unit Conversion with Mixed Metric Units

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Which unit should I convert everything to?

How do I remember the conversion factors?

What if I get confused with the decimal conversions?

Can I convert to a different unit like cm instead?

How do I check if my final order is correct?

🌟 Unlock Your Math Potential

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