Order Mixed Metric Units: Comparing 0.06m, 9cm, 70mm, and 0.08dm

Unit Conversion with Mixed Metric Lengths

Order from smallest to largest:

0.06 0.06 m, 9 9 cm, 70 70 mm, 0.08 0.08 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:

0.06 0.06 m, 9 9 cm, 70 70 mm, 0.08 0.08 dm

2

Step-by-step solution

To solve this problem, we'll convert all the lengths to meters so that they can be directly compared:

  • Convert 0.060.06 m to meters.
    Since it's already in meters, it remains 0.060.06 m.

  • Convert 99 cm to meters.
    Since 11 cm equals 0.010.01 m, 99 cm equals 9×0.01=0.099 \times 0.01 = 0.09 m.

  • Convert 7070 mm to meters.
    Since 11 mm equals 0.0010.001 m, 7070 mm equals 70×0.001=0.0770 \times 0.001 = 0.07 m.

  • Convert 0.080.08 dm to meters.
    Since 11 dm equals 0.10.1 m, 0.080.08 dm equals 0.08×0.1=0.0080.08 \times 0.1 = 0.008 m.

Now, we can list them in ascending order of meters:

1. 0.080.08 dm = 0.0080.008 m
2. 0.060.06 m
3. 7070 mm = 0.070.07 m
4. 99 cm = 0.090.09 m

Therefore, ordered from smallest to largest, the measurements are:

0.080.08 dm
0.060.06 m
7070 mm
99 cm

3

Final Answer

0.08 0.08 dm
0.06 0.06 m
70 70 mm
9 9 cm

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Convert all measurements to the same unit for comparison
  • Technique: Use common unit like meters: 9 9 cm = 0.09 0.09 m
  • Check: Compare decimal values: 0.008<0.06<0.07<0.09 0.008 < 0.06 < 0.07 < 0.09

Common Mistakes

Avoid these frequent errors
  • Comparing measurements without converting to same unit
    Don't compare 70 mm directly to 9 cm = wrong order! Different units have different values even if numbers look similar. Always convert all measurements to the same unit first, then compare the decimal values.

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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Any unit works, but meters are often easiest because most conversions result in simple decimals. You could also use millimeters if you prefer whole numbers!

How do I remember the metric conversion factors?

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Remember that each step moves the decimal point: mm → cm (÷10), cm → dm (÷10), dm → m (÷10). So mm → m means divide by 1000!

What if I get confused about which direction to convert?

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Think about size: smaller units need bigger numbers. So 1 meter = 1000 mm because millimeters are much smaller than meters.

Can I convert to a different unit like centimeters instead?

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Absolutely! Converting to centimeters: 0.08 0.08 dm = 0.8 0.8 cm, 0.06 0.06 m = 6 6 cm, 70 70 mm = 7 7 cm, 9 9 cm stays 9 9 cm.

Why does 0.08 dm become the smallest when 0.08 looks bigger than 0.06?

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Because decimeters are smaller than meters! 0.08 0.08 dm = 0.008 0.008 m, which is much smaller than 0.06 0.06 m. Always convert first!

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