 with only 16 decimal digits of
accuracy,</p>
<pre><code>1 + 1e-20 == 1</code></pre>
<p>The closest floating point number to <span class="math inline">\(1 + 10^{-20}\)</span> turns out to be
<span class="math inline">\(1\)</span> itself. By contrast, <code>0 + 1e-20 == 1e-20</code>.</p>
<p>This highlights the fact that precision depends on scale. Even though
<code>1 + 1e-20 == 1</code>, we have <code>1e-20 + 1e-20 == 2e-20</code>, as expected.</p>
<p>Rounding also manifests itself in a lack of <em>transitiv