Ordering Length Measurements: 0.2m, 35mm, 15cm, and 0.05dm Comparison

Unit Conversion with Mixed Metric Measurements

Order from smallest to largest:

0.2 0.2 m, 35 35 mm, 15 15 cm, 0.05 0.05 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:

0.2 0.2 m, 35 35 mm, 15 15 cm, 0.05 0.05 dm

2

Step-by-step solution

To order the given lengths from smallest to largest, we need to convert each measurement into meters:

  • 35 mm 35 \text{ mm} : Convert using 35 mm×0.001=0.035 m 35 \text{ mm} \times 0.001 = 0.035 \text{ m} .
  • 15 cm 15 \text{ cm} : Convert using 15 cm×0.01=0.15 m 15 \text{ cm} \times 0.01 = 0.15 \text{ m} .
  • 0.05 dm 0.05 \text{ dm} : Convert using 0.05 dm×0.1=0.005 m 0.05 \text{ dm} \times 0.1 = 0.005 \text{ m} .
  • 0.2 m 0.2 \text{ m} is already in meters.

After conversion, we have:

  • 0.035 m 0.035 \text{ m} from 35 mm
  • 0.15 m 0.15 \text{ m} from 15 cm
  • 0.005 m 0.005 \text{ m} from 0.05 dm
  • 0.2 m 0.2 \text{ m} .

Next, arrange these values from smallest to largest:

  • 0.005 m 0.005 \text{ m} from 0.05 dm 0.05 \text{ dm}
  • 0.035 m 0.035 \text{ m} from 35 mm 35 \text{ mm}
  • 0.15 m 0.15 \text{ m} from 15 cm 15 \text{ cm}
  • 0.2 m 0.2 \text{ m} from 0.2 m 0.2 \text{ m} .

The ordering from smallest to largest is 0.05 dm 0.05 \text{ dm} , 35 mm 35 \text{ mm} , 15 cm 15 \text{ cm} , 0.2 m 0.2 \text{ m} .

Therefore, the correct order is choice 1:

0.05 0.05 dm
35 35 mm
15 15 cm
0.2 0.2 m

3

Final Answer

0.05 0.05 dm
35 35 mm
15 15 cm
0.2 0.2 m

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Convert all measurements to same unit before comparing
  • Technique: 35 mm = 0.035 m using multiplication by 0.001
  • Check: Order the converted values: 0.005 < 0.035 < 0.15 < 0.2 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing numbers without converting units first
    Don't compare 0.2, 35, 15, and 0.05 directly = wrong order! These numbers have different units (m, mm, cm, dm) so their values can't be compared. Always convert all measurements to the same unit before ordering.

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?

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You can convert to any unit, but meters work well since it's the base unit. You could also convert everything to millimeters or centimeters - you'll get the same final order!

How do I remember the conversion factors?

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Think of the metric ladder: km → m → dm → cm → mm. Each step down multiplies by 10. So: 1 m = 10 dm = 100 cm = 1000 mm.

What if I forget whether to multiply or divide?

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Ask yourself: "Am I going to a bigger or smaller unit?" Bigger units have smaller numbers, so multiply. Smaller units have bigger numbers, so divide.

Can I convert to different units for each measurement?

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No! You must convert all measurements to the same unit to compare them properly. Mixing units will give you the wrong order.

Why is 0.05 dm the smallest when 0.05 looks bigger than 0.2?

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Because 0.05 dm = 0.005 m, which is much smaller than 0.2 m! The unit makes all the difference - always convert before comparing.

How can I check if my conversions are right?

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Use estimation! 35 mm is about the width of a paperclip, 15 cm is about a ruler width, 0.2 m is 20 cm. Does your order make sense with real objects?

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