Compare and Order: 55mm, 0.5cm, 0.007m, and 0.09dm from Smallest to Largest

Unit Conversion with Mixed Metric Measurements

Order from smallest to largest:

55 55 mm, 0.5 0.5 cm, 0.007 0.007 m, 0.09 0.09 dm

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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:

55 55 mm, 0.5 0.5 cm, 0.007 0.007 m, 0.09 0.09 dm

2

Step-by-step solution

Let's begin by converting each measurement to millimeters:

  • 55 55 mm is already in millimeters, so it stays at 55 55 mm.
  • 0.5 0.5 cm = 0.5×10 0.5 \times 10 mm = 5 5 mm.
  • 0.007 0.007 m = 0.007×1000 0.007 \times 1000 mm = 7 7 mm.
  • 0.09 0.09 dm = 0.09×100 0.09 \times 100 mm = 9 9 mm.

Now, comparing these converted lengths in millimeters:

  • The smallest value is 5 5 mm which corresponds to 0.5 0.5 cm.
  • The next smallest is 7 7 mm which corresponds to 0.007 0.007 m.
  • The third is 9 9 mm which corresponds to 0.09 0.09 dm.
  • The largest is 55 55 mm which corresponds directly to 55 55 mm.

Therefore, in ascending order, the lengths are:

0.5 0.5 cm
0.007 0.007 m
0.09 0.09 dm
55 55 mm

3

Final Answer

0.5 0.5 cm
0.007 0.007 m
0.09 0.09 dm
55 55 mm

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Convert all measurements to same unit before comparing
  • Technique: Use conversion factors: 1 cm = 10 mm, 1 m = 1000 mm, 1 dm = 100 mm
  • Check: Verify order by converting back: 5 mm < 7 mm < 9 mm < 55 mm ✓

Common Mistakes

Avoid these frequent errors
  • Comparing measurements in different units
    Don't compare 55 mm directly to 0.5 cm without converting = wrong order! Different units have different scales, so 55 looks bigger than 0.5 even though they're not in the same unit. Always convert everything to the same unit first.

Practice Quiz

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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 smallest unit in your list! In this case, millimeters (mm) is smallest, so convert everything to mm. This avoids decimals and makes comparison easier.

How do I remember the conversion factors?

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Think of the metric ladder: each step is ×10. From m to dm to cm to mm, you multiply by 10 each time. So 1 m = 1000 mm (×10×10×10).

What if I convert to a different unit like meters?

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That's fine too! You'll get: 0.005 0.005 m, 0.007 0.007 m, 0.009 0.009 m, 0.055 0.055 m. The order stays the same!

Why is 55 mm bigger than 0.007 m when 55 is much bigger than 0.007?

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Don't compare the numbers - compare the actual lengths! When you convert: 55 mm stays 55 mm, but 0.007 m = 7 mm. Now you can see 55 mm > 7 mm.

Can I use a calculator for these conversions?

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Absolutely! Metric conversions are just multiplication. But try to learn the basic factors (×10, ×100, ×1000) so you can do simple ones in your head.

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