MTH3051 Introduction to Computational Mathematics - User Web ...

School of Mathematical Sciences
Monash University
3.7 Addition
0 . 1 2 3 4 5 6 7 8 9 0
0 . 5 6 7 8 1 2 3 4 5 6
0 . 6 9 1 2 6 9 1 3 4 6
From this we observe (assuming no carries)
E R (x + y) = E R (x) + E R (y)
= 10 −N O (x) + 10 −N O (y)
= 10 −N O (x + y) (since x, y > 0)
So we expect N digits in the final answer – i.e. no loss of significant digits.
Example 3.10
Given that ˜z is the numerical result for z = x + y, how many digits in ˜z can we take
as being exactly correct? Which digits might be in error (and why)? Hint: think about
carries (if any).
3.8 Subtraction
Let us suppose that the first Q digits of x and y match
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