What is the result of 3-digit chopping for 0.000234?

Question

I am trying to understand if the 0."000" part counted as digit or not.

If 0."000" is not "digit", then the result should 0.000234. If yes, then the result should be 0.00

Which one is correct?

---

Here's the definition of chopping from my textbook:

Answer 1

Either could be the correct action to take, depending on the calculation you are doing. If you are adding it to a number with three figures past the decimal point like $1.234$ you should also keep three past the decimal and get $0.000$. If you are multiplying it by something with three significant figures, like $123,000$ you should keep three significant figures and get $0.000234$. I don't know the official definition of "3 digit chopping" so cannot comment on which is intended.

In the definition you copied from the textbook it refers to the mantissa of the number. The mantissa is the number after you put the first digit in a standard position by multiplying by the proper power of $10$. This is called the floating point form. Your text then talks about chopping the mantissa, so the proper result is $0.234\cdot 10^{-3}$

Answer 2

It has been a while, but hopefully, students in the future will benefit from my answer.

My book has a very similar definition but adds a couple of details. It says that d_1 can be from 1 to 9 and d_i can be from 0 to 9. So 0.000234 would be expressed as 0.234*10^-3. As a result, the three-digit chopping for 0.000234 would be itself, 0.000234.

The book I am using is Numerical Analysis, by Burden, Faires, Burden, 10th edition. Yours might be a slightly older version for it to have such a similar definition.