Box 3-2 Propagation of Uncertainty in the Product

But what if we just apply the multiplication formula 3-6 to the product x x  

Which uncertainty is correct, 6% from Table 3-1 or 4.2% from Equation 3-6  

Equation 3-6 presumes that the uncertainty in each factor of the product x z is random and independent of the other. In the product x z, the measured value of x could be high sometimes and the measured value of z could be low sometimes. In the 

Example. The distance traveled by a falling object in time t is gt2, where g is the acceleration of gravity. If t has an uncertainty of 1%, the uncertainty in t2 is 2(%e,) = 2(1%) = 2%. The uncertainty in distance computed from gt1 will also be 2%. If you (incorrectly) used Equation 3-6, you would compute an uncertainty in distance of Vl %2 + 1 %2 = 1.4%. 

Appendix C gives a general rule for propagation of random uncertainty for any function. 

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