# Numerical precision

**URL:** <https://discourse.julialang.org/t/numerical-precision/78749>\
**Category:** General Usage\
**Tags:** question, precision\
**Created:** [March 30, 2022, 2:43pm UTC](https://discourse.julialang.org/t/numerical-precision/78749 "2022-03-30T14:43:38Z")\
**Posts on this page:** 1\
**Showing post:** 7

<div class="post-metadata">

**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [March 30, 2022, 6:06pm UTC](https://discourse.julialang.org/t/numerical-precision/78749/7 "2022-03-30T18:06:09Z")

</div>

> [@rafael.guerra](#):
>
> Results will behave by using big floats.

@F-YF posted an ill-conditioned sum whose terms (in exact arithmetic) should _exactly_ cancel to give zero. _Any_ roundoff error can give a nonzero answer, which is an _infinite_ relative error compared to `0.0` (_no_ digits are correct), no matter how much precision you have.

(From another perspective, compared to the magnitude of the _summand terms_ \sim 1/x^6 \approx 10^{58}, an error of 10^{43} is quite small: 10^{43} / 10^{58} = 10^{-15}.)

This is exactly the same as the issue discussed in another thread here: ["sum([1.0, 1e100, 1.0, -1e100])" fails - #10 by stevengj](https://discourse.julialang.org/t/sum-1-0-1e100-1-0-1e100-fails/76502/10)

---

_[View the full topic](https://discourse.julialang.org/t/numerical-precision/78749)._