Order Length Units: Converting 2cm, 0.4dm, 30mm, and 0.01m

Unit Conversion with Mixed Length Measurements

Order from smallest to largest:

2 2 cm, 0.4 0.4 dm, 30 30 mm, 0.01 0.01 m

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Order from smallest to largest:

2 2 cm, 0.4 0.4 dm, 30 30 mm, 0.01 0.01 m

2

Step-by-step solution

To order the given lengths from smallest to largest, we first convert all measurements to a common unit, such as centimeters:

  • 22 cm is already in centimeters.
  • 0.40.4 dm: Using the conversion 11 dm = 1010 cm, 0.40.4 dm = 0.4×10=40.4 \times 10 = 4 cm.
  • 3030 mm: Using the conversion 11 mm = 0.10.1 cm, 3030 mm = 30×0.1=330 \times 0.1 = 3 cm.
  • 0.010.01 m: Using the conversion 11 m = 100100 cm, 0.010.01 m = 0.01×100=10.01 \times 100 = 1 cm.

Now, we can arrange the lengths in ascending order by their converted measurements:

  • 0.010.01 m = 11 cm
  • 22 cm = 22 cm
  • 3030 mm = 33 cm
  • 0.40.4 dm = 44 cm

Therefore, the correct order from smallest to largest is:

0.01 0.01 m
2 2 cm
30 30 mm
0.4 0.4 dm

3

Final Answer

0.01 0.01 m
2 2 cm
30 30 mm
0.4 0.4 dm

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert all units to the same base unit first
  • Technique: Use standard conversions like 0.4 0.4 dm = 0.4×10=4 0.4 \times 10 = 4 cm
  • Check: Verify by comparing converted values: 1 cm < 2 cm < 3 cm < 4 cm ✓

Common Mistakes

Avoid these frequent errors
  • Comparing different units without converting
    Don't compare 2 cm to 0.4 dm directly without converting = wrong order! Different units have different scales, so 0.4 looks smaller than 2 but is actually larger. Always convert everything to the same unit first.

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?

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Choose the unit that makes calculations easiest! Centimeters work well here because most conversions avoid decimals. You could also use millimeters, but you'd get larger numbers.

How do I remember the conversion factors?

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Use the metric ladder! From largest to smallest: meter → decimeter → centimeter → millimeter. Each step down multiplies by 10, each step up divides by 10.

What if I convert to the wrong unit?

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No problem! As long as you convert all measurements to the same unit consistently, you'll get the correct order. The relative sizes stay the same.

Can I just estimate instead of converting exactly?

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Be careful! Estimating works for obvious differences, but 2 2 cm vs 30 30 mm are very close (2 cm vs 3 cm). Always convert for accuracy.

Why does 0.01 m equal 1 cm?

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Because 1 1 meter = 100 100 centimeters, so 0.01×100=1 0.01 \times 100 = 1 cm. Think of it as 1 hundredth of a meter equals 1 centimeter!

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