I am on example 1.8 in University physics 13th (Freedman/Young) and have a quest

Question

I am on example 1.8 in University physics 13th (Freedman/Young) and have a question regarding sig figs. I am trying to calculate the magnitude of a displacement vector using the following components: Ax= -10.4km; Ay= 8.7km; Az=2.1 km. Taking the square root of ((Ax)^2)+((Ay)^2))+((Az)^2))=13.72078715. The book rounds this off to 13.7 and I am just wondering why they chose to include 3 sig figs. Shouldn't it technically only be 2 sig figs? (ie 14) since the smallest component value has only 2 significant figures?
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Source:ISBN: 0321850025 | Title: University Physics with Modern Physics | Publisher: Addison Wesley

Explanation / Answer

Actually i don't know any rule about taking the sig figs of the smallest component value and rounding off to it, but a general rule given by my lab instructor says that the final result and all intermediate calculations should always be rounded off to minimum of the no. of decimal positions of all input variable values.

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