Significant Figures: Cylinder Volume Calculation

[zorro]

Homework Statement

The length of a cylinder is 1.2 x 10^-2 m and its radius is 2.12 x 10^-2 m. What is its volume according to significicant figures?

Homework Equations

The Attempt at a Solution

V=(pi)r^2 l
r^2 = 4.49 x 10^-4 (as radius has 3 significant digits)
V= 22/7 x 4.49 x 10^-4 x 1.2 x 10^-2
V= 22/7 x 5.4 x 10^-6 [4.49 x 10^-4 x 1.2 x 10^-2 = 5.388 x 10^-6 = 5.4 x 10^-6 as least no. of significant digits is 2 here)
so V=1.7 x 10^-5

Answer is 16.9 x 10^-6

 

[Borek]

1.7x10^-5 m³ looks correct to me. But you should not use 22/7 for pi nor round down intermediate results.

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[zorro]

Intermediate results have to be rounded off in order to satisfy the rules of significant figures.

 

[Borek]

No. You should round them down only if you are displaying them, but you do the calculations using full accuracy.

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[zorro]

you mean to say that
5.388 x 10^-6 = 5.4 x 10^-6
should be written as 5.3 x 10^-6 ?

 

[Borek]

No, when displaying it should be written as 5.4x10^-5, but for calculations you should use 5.388x10^-5.

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