Mystery Dog Heights

The heights of these dogs are in very different units. Our only solution is to convert the height of each of the dogs to a shared unit so that we can compare them. For example, we can convert all of the dogs' heights to inches.

We convert Chloe's height to inches as follows:

If we convert the heights of the other dogs to inches their heights become:

• Zorro: $11.5 \textrm{ in}$
• Duke: $\SI{660.4}{\milli\meter} \ce{->} 26 \textrm{ in}$
• Chloe: $\SI{47}{\centi\meter} \ce{->} 18.48 \textrm{ in}$
• Xiaomei: $0.625 \textrm{ ft} \ce{->} 7.5 \textrm{ in}$

We can then rearrange the dogs in order of smallest to largest as follows:

• Xiaomei: $7.5 \textrm{ in}$
• Zorro: $11.5 \textrm{ in}$
• Chloe: $18.48 \textrm{ in}$
• Duke: $26 \textrm{ in}$

1 inch = 25.4 mm

1 cm = 10 mm

12 inches = 1 ft

Since Zorro is the first on the list and Zorro's height is in inches, convert the heights of the other dogs to inches.

$Duke: 660.4~mm \left(\dfrac{1~inch}{25.4~mm}\right)=26~ inches$

$Chloe: 47~cm \left(\dfrac{10~mm}{1~cm}\right)\left(\dfrac{1~in}{25.4~mm}\right) \approx 18.5~inches$

$Xiaomet: 0.625~ft\left(\dfrac{12~in}{1~ft}\right) = 7.5~inches$

So the arrangement from shortest to tallest is

$Xiaomet, Zorro,Chloe$ then $Duke$ .

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Marvin