Exploring 3-Digit Floating Point Arithmetic: What is it and How Does it Work?

[brandy]

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]

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).

 

[brandy]

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]

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]

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]

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.