# What is 3 digit arithmetic?

what is 3(or i, where i=1,2,3,4......∞) digit arithmetic? is it just working with 3 decimals or 3 significant figures? or is it base 3 arithmetic?

DaveC426913
Gold Member
what is 3(or i, where i=1,2,3,4......∞) digit arithmetic? is it just working with 3 decimals or 3 significant figures? or is it base 3 arithmetic?
Context?

The expression could mean anything.

But if I heard someone say they could do 3 digit arithmetic, I would assume they could add subtract and multiply 3-digit numbers (100-999).

the context was talking about floating point numbers and catastrophic cancellation in the quadratic equation.

it said using 3 digit arithmetic:
*subs in some numbers, 0.2, 100.9 etc into the quad equation and at the end rounds the entire number to 3 digits*

am i right in assuming that all the numbers used to input had to be 3 decimals and then the final number had to be 3 digits?
or does every number in the process have to be rounded to 3 decimals as the number is created? step by step?

HallsofIvy
Homework Helper
Of course, any decent calculator or computer will carry 12 or more digits for its calculations. But just to give a simple example, that a human could calculate easily, of how cancellation happens, they are restricting to three digits. I don't see any difference between using three digits from the outset and rounding to three digits.

DaveC426913
Gold Member
I don't see any difference between using three digits from the outset and rounding to three digits.
What? Of course there's a difference.

Mark44
Mentor
Since the context is floating point arithmetic, my guess at what you're asking is that numbers are represented by a 3-digit mantissa and an exponent.

Using the numbers you gave as examples, 0.2 would be 2.00 x 10-1 and 100.9 would be 1.01 x 102.

If you want a better answer, you'll need to ask a question that is clearer.