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This isn't a homework question, but instead a question about an example in a book I'm reading, in prep for next semester. As such using the posting template is a bit of a miss. Hope that can be forgiven.

I'm reading "An Introduction to Error Analysis" by John R Taylor during my spring vacation as brush up for my next semester. I encountered an example that doesn't make sense to me though. It goes through teaching 3 rules as follows:

(3.8)

(3.9)

(3.10)

Now the example it gives is as follows (leaving out units for ease):

##t = 1.6\pm0.1##

##h = 46.2\pm0.3##

Now it calculates ##g = \frac{2*h}{t^2}## and more importantly its uncertainty as follows:

$$\frac{\delta g}{g}=\frac{\delta h}{h}+2*\frac{\delta t}{t} = 0.007+2*0.063 = 0.133$$

as justifed by 3.8 and 3.10. However here is my problem; What about 3.9?

As far as I can see, the example completely forgets about the factor 2. With 3.9 in mind, ##x = \frac{h}{t^2}## shouldn't it be:

$$\frac{\delta g}{g}=2*\left(\frac{\delta h}{h}+2*\frac{\delta t}{t}\right)$$

What am I missing?

1. Homework Statement1. Homework Statement

I'm reading "An Introduction to Error Analysis" by John R Taylor during my spring vacation as brush up for my next semester. I encountered an example that doesn't make sense to me though. It goes through teaching 3 rules as follows:

Now the example it gives is as follows (leaving out units for ease):

##t = 1.6\pm0.1##

##h = 46.2\pm0.3##

Now it calculates ##g = \frac{2*h}{t^2}## and more importantly its uncertainty as follows:

$$\frac{\delta g}{g}=\frac{\delta h}{h}+2*\frac{\delta t}{t} = 0.007+2*0.063 = 0.133$$

as justifed by 3.8 and 3.10. However here is my problem; What about 3.9?

## The Attempt at a Solution

As far as I can see, the example completely forgets about the factor 2. With 3.9 in mind, ##x = \frac{h}{t^2}## shouldn't it be:

$$\frac{\delta g}{g}=2*\left(\frac{\delta h}{h}+2*\frac{\delta t}{t}\right)$$

What am I missing?