Converting and Ordering: 11cm, 0.1dm, 90mm, and 0.011m from Smallest to Largest

Q: Which unit should I convert everything to?

Choose the unit that appears most frequently or the one you're most comfortable with. In this problem, centimeters work well since most values convert to whole numbers or simple decimals.

Q: How do I remember the conversion factors?

Remember the basic pattern: meter → decimeter → centimeter → millimeter. Each step is ×10: 1 m = 10 dm = 100 cm = 1000 mm. Going backwards means ÷10.

Q: What if I get confused about multiplying vs dividing?

Think logically: when converting to a smaller unit, you get more pieces, so multiply. When converting to a larger unit, you get fewer pieces, so divide.

Q: Why does 0.011 m equal 1.1 cm?

Since 1 meter = 100 centimeters, multiply by 100: $ 0.011 \times 100 = 1.1 $ cm. The decimal point moves two places to the right.

Q: Can I use a different method to solve this?

Yes! You could convert everything to millimeters or meters instead. The key is being consistent - use the same unit for all measurements before comparing.

Q: How do I avoid making calculation errors?

Write out each conversion step clearly and double-check your arithmetic. For example: $ 90 \text{ mm} ÷ 10 = 9 \text{ cm} $. Then verify: $ 9 \times 10 = 90 $ ✓

Metric Unit Conversion with Mixed Units

Order from smallest to largest:

$11$ cm, $0.1$ dm, $90$ mm, $0.011$ m

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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:

$11$ cm, $0.1$ dm, $90$ mm, $0.011$ m

Step-by-step solution

To solve this problem, we'll convert each given length to centimeters:

The length $11$ cm is already in centimeters.
The length $0.1$ dm; knowing $1$ dm = $10$ cm, gives $0.1 \times 10 = 1$ cm.
The length $90$ mm; knowing $1$ cm = $10$ mm, gives $90 / 10 = 9$ cm.
The length $0.011$ m; knowing $1$ m = $100$ cm, gives $0.011 \times 100 = 1.1$ cm.

Now, we list the lengths in centimeters:

$0.1$ dm = $1$ cm
$0.011$ m = $1.1$ cm
$90$ mm = $9$ cm
$11$ cm = $11$ cm

The correct order from smallest to largest is:

$0.1$ dm
$0.011$ m
$90$ mm
$11$ cm

Therefore, the order from smallest to largest is: $0.1$ dm, $0.011$ m, $90$ mm, $11$ cm.

Comparing with the options provided, the correct choice is option 2.

Final Answer

$0.1$ dm
$0.011$ m
$90$ mm
$11$ cm

Key Points to Remember

Essential concepts to master this topic

Strategy: Convert all measurements to the same unit before comparing
Technique: Use conversion factors: 1 dm = 10 cm, 1 m = 100 cm, 1 cm = 10 mm
Check: Verify order by comparing converted values: 1 < 1.1 < 9 < 11 ✓

Common Mistakes

Avoid these frequent errors

Comparing different units without converting
Don't compare 11 cm directly to 0.1 dm without converting = wrong order! Different units have different scales, so 0.1 looks smaller than 11 but represents the same magnitude. Always convert all measurements to the same unit first.

Practice Quiz

Test your knowledge with interactive questions

Convert to cm:
$$ 0.6 $$ meters

FAQ

Everything you need to know about this question

Which unit should I convert everything to?

Choose the unit that appears most frequently or the one you're most comfortable with. In this problem, centimeters work well since most values convert to whole numbers or simple decimals.

How do I remember the conversion factors?

Remember the basic pattern: meter → decimeter → centimeter → millimeter. Each step is ×10: 1 m = 10 dm = 100 cm = 1000 mm. Going backwards means ÷10.

What if I get confused about multiplying vs dividing?

Think logically: when converting to a smaller unit, you get more pieces, so multiply. When converting to a larger unit, you get fewer pieces, so divide.

Why does 0.011 m equal 1.1 cm?

Since 1 meter = 100 centimeters, multiply by 100: $0.011 \times 100 = 1.1$ cm. The decimal point moves two places to the right.

Can I use a different method to solve this?

Yes! You could convert everything to millimeters or meters instead. The key is being consistent - use the same unit for all measurements before comparing.

How do I avoid making calculation errors?

Write out each conversion step clearly and double-check your arithmetic. For example: $90 \text{ mm} ÷ 10 = 9 \text{ cm}$ . Then verify: $9 \times 10 = 90$ ✓

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Converting and Ordering: 11cm, 0.1dm, 90mm, and 0.011m from Smallest to Largest

Metric Unit Conversion with Mixed 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 about multiplying vs dividing?

Why does 0.011 m equal 1.1 cm?

Can I use a different method to solve this?

How do I avoid making calculation errors?

🌟 Unlock Your Math Potential

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