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A micrometer is one-millionth of a meter (0.000001): ten thousand times shorter than a centimeter (0.01). How many micrometer one is one edge of a centimeter cube?

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If a cube has an edge of one centimeter and one centimeter is ten thousand times longer than a micrometer, then the edge has ten thousand micrometers.

I hope that's what you meant :)

Answer:

       [tex]1cm^3=0.000000000001mm^3[/tex]

Step-by-step explanation:

Given :  0.000001 mm = 0.01 cm

To find : How many [tex]mm^3[/tex] is in [tex]1 cm^3[/tex]

Solution :

Step 1 : Given  0.000001 mm = 0.01 cm

Step 2: Cubing both side [tex](0.000001mm)^3 = (0.01cm)^3[/tex]

Step 3: Solve  [tex](10^{-6})^3mm^3=(10^{-2})^3cm^3[/tex]

                    [tex]\Rightarrow\frac{(10^{-6})^3}{(10^{-2})^3}mm^3=1cm^3[/tex]

                    [tex]\Rightarrow\frac{10^{-18}}{10^{-6}}mm^3=1cm^3[/tex]

                    [tex]\Rightarrow 10^{-18+6}mm^3=1cm^3[/tex]

                    [tex]\Rightarrow 10^{-12}mm^3=1cm^3[/tex]

                     [tex]\Rightarrow 0.000000000001mm^3=1cm^3[/tex]

 Therefore,  [tex]1cm^3=0.000000000001mm^3[/tex]

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