Errata for Thomas' Calculus

Jimmy Snyder

I have a copy of the book Thomas' Calculus Early Trancendentals Media Upgrade 11th edition. I have found a couple of errata. While neither of them is important, I found them entertaining.

On page 179 at the bottom right hand corner there is what purports to be a multiflash photograph of falling balls. This cannot be a photograph but perhaps is an artist's rendition. Near the top of the figure, the later images of the falling balls appear beneath the earlier ones.

On page 242 in the middle of the page it says "the linearization gives 2 as the approximation for [tex]\sqrt{3}[/tex], which is not even accurate to one decimal place." I assume the author means that since the first digit of the square root is 1, 2 is off even in this place. However, it is necessary to round off the square root before making the comparison. Otherwise we would say that 2 is a terrible approximation to 1.9999999999999, it is not even accurate to one decimal place.

Ryker

It's cool you find errata entertaining and all, but you're off on this one. 2 is accurate to one decimal place in regards to 1.9999999999999, and I don't see anything wrong with the statement in the book. 1.7 as the approximation of the square root of 3 would be an example of a figure accurate to one decimal place.

I don't have the book, so I can't comment on the first "error" you mentioned.

Jimmy Snyder

Is 2 accurate to one decimal place in regards to 1.73?

Ryker

Like mentioned in the book and in my post, it's not.

Jimmy Snyder

So as I understand it, If I approximate 1.9999999999999 with 2, that's accurate to 1 decimal place. If I approximate 2.0000000000001 with 2, how many decimal places?

If I approximate 2001 with 2000, how many decimal places of accuracy would you assign it?

Jimmy Snyder

Anyway, I stand by my original post. I say that 2 approximates 1.9999999999999 to many decimal places and therefore, 2 approximates [tex]\sqrt{3}[/tex] to one decimal place. After all how would you approximate 173 to 1 decimal place?

Ryker

Yes, although this is accurate to more than one decimal place, same with 2.0000000000001.None.By, say, 173.03, 172.99, 173.343444444444444444444444444444444 etc.

Jimmy Snyder

You have to count the decimal places on both sides of the decimal point.

Ryker

Decimals do not equal significant digits.

Jimmy Snyder

That's pedantry and doesn't fit with what the author meant.

Jimmy Snyder

There is a pair of errata in the book Thomas' Calculus Early Trancendentals Media Upgrade 11th edition. On page 242 in the middle of the page it says "the linearization gives 2 as the approximation for [tex]\sqrt{3}[/tex], which is not even accurate to one decimal place." The author means "not even accurate to one significant digit." That's the first erratum. He's wrong. It is accurate to one significant digit. That's the second erratum.

Ryker

What's pedantry? All I'm saying is the author's statement that 2 is not accurate to one decimal place of the square root of 3 is perfectly correct, I'm not debating its context. And the statement also doesn't hinge on the fact that the square root of 3 starts with a 1 instead of a 2 (well, in this particular case it does, but only indirectly, as the first decimal is 7).

Ryker

How do you know he means that it's accurate to one significant digit. In this case, he would indeed be wrong, but if he meant one decimal place, then he is right.

Jimmy Snyder

Because it makes no sense to focus on the digits to the right of the decimal place when there is a discrepency on the left.

Ryker

Of course it makes sense. 2 in regards to 1.96 is accurate to one decimal place, even though 1.96 starts with 1. 2 in regards to 1.73 isn't, but the fact that 1.73 starts with 1 alone isn't the reason for this. I think you're not getting the concept of accuracy to one decimal place.

Jimmy Snyder

OK, I see what you are saying. However the book is still wrong. The number of accurate decimals places is not an issue when it comes to accuracy. You pointed out yourself that 2000 as an approximation 2001 is not accurate to a single decimal place. So the author may well have meant decimal places, but he shouldn't have. Accuracy is always a matter of significant digits, not necessarily of places to the right of the decimal point.

Ryker

No, the author is still right. In this specific case, you're comparing to the square root of 3, so accurate to one decimal place just means accurate to two significant digits.