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<li class="right"> <div class="inline-search" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" aria-label="Quick search" type="search" name="q" id="search-box" /> <input type="submit" value="Go" /> </form> </div> | </li> <li class="right"> <label class="theme-selector-label"> Theme <select class="theme-selector" oninput="activateTheme(this.value)"> <option value="auto" selected>Auto</option> <option value="light">Light</option> <option value="dark">Dark</option> </select> </label> |</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <section id="module-fractions"> <span id="fractions-rational-numbers"></span><h1><a class="reference internal" href="#module-fractions" title="fractions: Rational numbers."><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code></a> — Rational numbers<a class="headerlink" href="#module-fractions" title="Link to this heading">¶</a></h1> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.12/Lib/fractions.py">Lib/fractions.py</a></p> <hr class="docutils" /> <p>The <a class="reference internal" href="#module-fractions" title="fractions: Rational numbers."><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code></a> module provides support for rational number arithmetic.</p> <p>A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string.</p> <dl class="py class"> <dt class="sig sig-object py" id="fractions.Fraction"> <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">fractions.</span></span><span class="sig-name descname"><span class="pre">Fraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">numerator</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">denominator</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction" title="Link to this definition">¶</a></dt> <dt class="sig sig-object py"> <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">fractions.</span></span><span class="sig-name descname"><span class="pre">Fraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other_fraction</span></span></em><span class="sig-paren">)</span></dt> <dt class="sig sig-object py"> <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">fractions.</span></span><span class="sig-name descname"><span class="pre">Fraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span></dt> <dt class="sig sig-object py"> <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">fractions.</span></span><span class="sig-name descname"><span class="pre">Fraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">decimal</span></span></em><span class="sig-paren">)</span></dt> <dt class="sig sig-object py"> <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">fractions.</span></span><span class="sig-name descname"><span class="pre">Fraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">string</span></span></em><span class="sig-paren">)</span></dt> <dd><p>The first version requires that <em>numerator</em> and <em>denominator</em> are instances of <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a> and returns a new <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with value <code class="docutils literal notranslate"><span class="pre">numerator/denominator</span></code>. If <em>denominator</em> is <code class="docutils literal notranslate"><span class="pre">0</span></code>, it raises a <a class="reference internal" href="exceptions.html#ZeroDivisionError" title="ZeroDivisionError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ZeroDivisionError</span></code></a>. The second version requires that <em>other_fraction</em> is an instance of <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a> and returns a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with the same value. The next two versions accept either a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> or a <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instance, and return a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with exactly the same value. Note that due to the usual issues with binary floating-point (see <a class="reference internal" href="../tutorial/floatingpoint.html#tut-fp-issues"><span class="std std-ref">Floating Point Arithmetic: Issues and Limitations</span></a>), the argument to <code class="docutils literal notranslate"><span class="pre">Fraction(1.1)</span></code> is not exactly equal to 11/10, and so <code class="docutils literal notranslate"><span class="pre">Fraction(1.1)</span></code> does <em>not</em> return <code class="docutils literal notranslate"><span class="pre">Fraction(11,</span> <span class="pre">10)</span></code> as one might expect. (But see the documentation for the <a class="reference internal" href="#fractions.Fraction.limit_denominator" title="fractions.Fraction.limit_denominator"><code class="xref py py-meth docutils literal notranslate"><span class="pre">limit_denominator()</span></code></a> method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">numerator</span> <span class="p">[</span><span class="s1">'/'</span> <span class="n">denominator</span><span class="p">]</span> </pre></div> </div> <p>where the optional <code class="docutils literal notranslate"><span class="pre">sign</span></code> may be either ‘+’ or ‘-’ and <code class="docutils literal notranslate"><span class="pre">numerator</span></code> and <code class="docutils literal notranslate"><span class="pre">denominator</span></code> (if present) are strings of decimal digits (underscores may be used to delimit digits as with integral literals in code). In addition, any string that represents a finite value and is accepted by the <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> constructor is also accepted by the <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">fractions</span> <span class="kn">import</span> <span class="n">Fraction</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="o">-</span><span class="mi">10</span><span class="p">)</span> <span class="go">Fraction(-8, 5)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mi">123</span><span class="p">)</span> <span class="go">Fraction(123, 1)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">()</span> <span class="go">Fraction(0, 1)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'3/7'</span><span class="p">)</span> <span class="go">Fraction(3, 7)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">' -3/7 '</span><span class="p">)</span> <span class="go">Fraction(-3, 7)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'1.414213 </span><span class="se">\t\n</span><span class="s1">'</span><span class="p">)</span> <span class="go">Fraction(1414213, 1000000)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'-.125'</span><span class="p">)</span> <span class="go">Fraction(-1, 8)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'7e-6'</span><span class="p">)</span> <span class="go">Fraction(7, 1000000)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">2.25</span><span class="p">)</span> <span class="go">Fraction(9, 4)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">1.1</span><span class="p">)</span> <span class="go">Fraction(2476979795053773, 2251799813685248)</span> <span class="gp">>>> </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="n">Decimal</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'1.1'</span><span class="p">))</span> <span class="go">Fraction(11, 10)</span> </pre></div> </div> <p>The <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> class inherits from the abstract base class <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a>, and implements all of the methods and operations from that class. <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instances are <a class="reference internal" href="../glossary.html#term-hashable"><span class="xref std std-term">hashable</span></a>, and should be treated as immutable. In addition, <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> has the following properties and methods:</p> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.2: </span>The <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> constructor now accepts <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> and <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instances.</p> </div> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.9: </span>The <a class="reference internal" href="math.html#math.gcd" title="math.gcd"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.gcd()</span></code></a> function is now used to normalize the <em>numerator</em> and <em>denominator</em>. <a class="reference internal" href="math.html#math.gcd" title="math.gcd"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.gcd()</span></code></a> always return a <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> type. Previously, the GCD type depended on <em>numerator</em> and <em>denominator</em>.</p> </div> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.11: </span>Underscores are now permitted when creating a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance from a string, following <span class="target" id="index-0"></span><a class="pep reference external" href="https://peps.python.org/pep-0515/"><strong>PEP 515</strong></a> rules.</p> </div> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.11: </span><a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> implements <code class="docutils literal notranslate"><span class="pre">__int__</span></code> now to satisfy <code class="docutils literal notranslate"><span class="pre">typing.SupportsInt</span></code> instance checks.</p> </div> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.12: </span>Space is allowed around the slash for string inputs: <code class="docutils literal notranslate"><span class="pre">Fraction('2</span> <span class="pre">/</span> <span class="pre">3')</span></code>.</p> </div> <div class="versionchanged"> <p><span class="versionmodified changed">Changed in version 3.12: </span><a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instances now support float-style formatting, with presentation types <code class="docutils literal notranslate"><span class="pre">"e"</span></code>, <code class="docutils literal notranslate"><span class="pre">"E"</span></code>, <code class="docutils literal notranslate"><span class="pre">"f"</span></code>, <code class="docutils literal notranslate"><span class="pre">"F"</span></code>, <code class="docutils literal notranslate"><span class="pre">"g"</span></code>, <code class="docutils literal notranslate"><span class="pre">"G"</span></code> and <code class="docutils literal notranslate"><span class="pre">"%""</span></code>.</p> </div> <dl class="py attribute"> <dt class="sig sig-object py" id="fractions.Fraction.numerator"> <span class="sig-name descname"><span class="pre">numerator</span></span><a class="headerlink" href="#fractions.Fraction.numerator" title="Link to this definition">¶</a></dt> <dd><p>Numerator of the Fraction in lowest term.</p> </dd></dl> <dl class="py attribute"> <dt class="sig sig-object py" id="fractions.Fraction.denominator"> <span class="sig-name descname"><span class="pre">denominator</span></span><a class="headerlink" href="#fractions.Fraction.denominator" title="Link to this definition">¶</a></dt> <dd><p>Denominator of the Fraction in lowest term.</p> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.as_integer_ratio"> <span class="sig-name descname"><span class="pre">as_integer_ratio</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.as_integer_ratio" title="Link to this definition">¶</a></dt> <dd><p>Return a tuple of two integers, whose ratio is equal to the original Fraction. The ratio is in lowest terms and has a positive denominator.</p> <div class="versionadded"> <p><span class="versionmodified added">New in version 3.8.</span></p> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.is_integer"> <span class="sig-name descname"><span class="pre">is_integer</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.is_integer" title="Link to this definition">¶</a></dt> <dd><p>Return <code class="docutils literal notranslate"><span class="pre">True</span></code> if the Fraction is an integer.</p> <div class="versionadded"> <p><span class="versionmodified added">New in version 3.12.</span></p> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.from_float"> <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_float</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">flt</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.from_float" title="Link to this definition">¶</a></dt> <dd><p>Alternative constructor which only accepts instances of <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> or <a class="reference internal" href="numbers.html#numbers.Integral" title="numbers.Integral"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Integral</span></code></a>. Beware that <code class="docutils literal notranslate"><span class="pre">Fraction.from_float(0.3)</span></code> is not the same value as <code class="docutils literal notranslate"><span class="pre">Fraction(3,</span> <span class="pre">10)</span></code>.</p> <div class="admonition note"> <p class="admonition-title">Note</p> <p>From Python 3.2 onwards, you can also construct a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance directly from a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>.</p> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.from_decimal"> <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_decimal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dec</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.from_decimal" title="Link to this definition">¶</a></dt> <dd><p>Alternative constructor which only accepts instances of <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> or <a class="reference internal" href="numbers.html#numbers.Integral" title="numbers.Integral"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Integral</span></code></a>.</p> <div class="admonition note"> <p class="admonition-title">Note</p> <p>From Python 3.2 onwards, you can also construct a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance directly from a <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instance.</p> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.limit_denominator"> <span class="sig-name descname"><span class="pre">limit_denominator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">max_denominator</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000000</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.limit_denominator" title="Link to this definition">¶</a></dt> <dd><p>Finds and returns the closest <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> to <code class="docutils literal notranslate"><span class="pre">self</span></code> that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number:</p> <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">fractions</span> <span class="kn">import</span> <span class="n">Fraction</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'3.1415926535897932'</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span> <span class="go">Fraction(355, 113)</span> </pre></div> </div> <p>or for recovering a rational number that’s represented as a float:</p> <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">pi</span><span class="p">,</span> <span class="n">cos</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">3</span><span class="p">))</span> <span class="go">Fraction(4503599627370497, 9007199254740992)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">3</span><span class="p">))</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span> <span class="go">Fraction(1, 2)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">1.1</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span> <span class="go">Fraction(11, 10)</span> </pre></div> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.__floor__"> <span class="sig-name descname"><span class="pre">__floor__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__floor__" title="Link to this definition">¶</a></dt> <dd><p>Returns the greatest <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> <code class="docutils literal notranslate"><span class="pre"><=</span> <span class="pre">self</span></code>. This method can also be accessed through the <a class="reference internal" href="math.html#math.floor" title="math.floor"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.floor()</span></code></a> function:</p> <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">floor</span> <span class="gp">>>> </span><span class="n">floor</span><span class="p">(</span><span class="n">Fraction</span><span class="p">(</span><span class="mi">355</span><span class="p">,</span> <span class="mi">113</span><span class="p">))</span> <span class="go">3</span> </pre></div> </div> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.__ceil__"> <span class="sig-name descname"><span class="pre">__ceil__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__ceil__" title="Link to this definition">¶</a></dt> <dd><p>Returns the least <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> <code class="docutils literal notranslate"><span class="pre">>=</span> <span class="pre">self</span></code>. This method can also be accessed through the <a class="reference internal" href="math.html#math.ceil" title="math.ceil"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.ceil()</span></code></a> function.</p> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.__round__"> <span class="sig-name descname"><span class="pre">__round__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__round__" title="Link to this definition">¶</a></dt> <dt class="sig sig-object py"> <span class="sig-name descname"><span class="pre">__round__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ndigits</span></span></em><span class="sig-paren">)</span></dt> <dd><p>The first version returns the nearest <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> to <code class="docutils literal notranslate"><span class="pre">self</span></code>, rounding half to even. The second version rounds <code class="docutils literal notranslate"><span class="pre">self</span></code> to the nearest multiple of <code class="docutils literal notranslate"><span class="pre">Fraction(1,</span> <span class="pre">10**ndigits)</span></code> (logically, if <code class="docutils literal notranslate"><span class="pre">ndigits</span></code> is negative), again rounding half toward even. This method can also be accessed through the <a class="reference internal" href="functions.html#round" title="round"><code class="xref py py-func docutils literal notranslate"><span class="pre">round()</span></code></a> function.</p> </dd></dl> <dl class="py method"> <dt class="sig sig-object py" id="fractions.Fraction.__format__"> <span class="sig-name descname"><span class="pre">__format__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">format_spec</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">/</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__format__" title="Link to this definition">¶</a></dt> <dd><p>Provides support for float-style formatting of <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instances via the <a class="reference internal" href="stdtypes.html#str.format" title="str.format"><code class="xref py py-meth docutils literal notranslate"><span class="pre">str.format()</span></code></a> method, the <a class="reference internal" href="functions.html#format" title="format"><code class="xref py py-func docutils literal notranslate"><span class="pre">format()</span></code></a> built-in function, or <a class="reference internal" href="../reference/lexical_analysis.html#f-strings"><span class="std std-ref">Formatted string literals</span></a>. The presentation types <code class="docutils literal notranslate"><span class="pre">"e"</span></code>, <code class="docutils literal notranslate"><span class="pre">"E"</span></code>, <code class="docutils literal notranslate"><span class="pre">"f"</span></code>, <code class="docutils literal notranslate"><span class="pre">"F"</span></code>, <code class="docutils literal notranslate"><span class="pre">"g"</span></code>, <code class="docutils literal notranslate"><span class="pre">"G"</span></code> and <code class="docutils literal notranslate"><span class="pre">"%"</span></code> are supported. For these presentation types, formatting for a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> object <code class="docutils literal notranslate"><span class="pre">x</span></code> follows the rules outlined for the <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> type in the <a class="reference internal" href="string.html#formatspec"><span class="std std-ref">Format Specification Mini-Language</span></a> section.</p> <p>Here are some examples:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">fractions</span> <span class="kn">import</span> <span class="n">Fraction</span> <span class="gp">>>> </span><span class="nb">format</span><span class="p">(</span><span class="n">Fraction</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">),</span> <span class="s1">'.40g'</span><span class="p">)</span> <span class="go">'0.1428571428571428571428571428571428571429'</span> <span class="gp">>>> </span><span class="nb">format</span><span class="p">(</span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'1234567.855'</span><span class="p">),</span> <span class="s1">'_.2f'</span><span class="p">)</span> <span class="go">'1_234_567.86'</span> <span class="gp">>>> </span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">Fraction</span><span class="p">(</span><span class="mi">355</span><span class="p">,</span><span class="w"> </span><span class="mi">113</span><span class="p">)</span><span class="si">:</span><span class="s2">*>20.6e</span><span class="si">}</span><span class="s2">"</span> <span class="go">'********3.141593e+00'</span> <span class="gp">>>> </span><span class="n">old_price</span><span class="p">,</span> <span class="n">new_price</span> <span class="o">=</span> <span class="mi">499</span><span class="p">,</span> <span class="mi">672</span> <span class="gp">>>> </span><span class="s2">"</span><span class="si">{:.2%}</span><span class="s2"> price increase"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">Fraction</span><span class="p">(</span><span class="n">new_price</span><span class="p">,</span> <span class="n">old_price</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="go">'34.67% price increase'</span> </pre></div> </div> </dd></dl> </dd></dl> <div class="admonition seealso"> <p class="admonition-title">See also</p> <dl class="simple"> <dt>Module <a class="reference internal" href="numbers.html#module-numbers" title="numbers: Numeric abstract base classes (Complex, Real, Integral, etc.)."><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code></a></dt><dd><p>The abstract base classes making up the numeric tower.</p> </dd> </dl> </div> </section> <div class="clearer"></div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <div> <h4>Previous topic</h4> <p class="topless"><a href="decimal.html" title="previous chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code> — Decimal fixed point and floating point arithmetic</a></p> </div> <div> <h4>Next topic</h4> <p class="topless"><a href="random.html" title="next chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a></p> </div> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li> <a href="https://github.com/python/cpython/blob/main/Doc/library/fractions.rst" rel="nofollow">Show Source </a> </li> </ul> </div> </div> <div id="sidebarbutton" title="Collapse sidebar"> <span>«</span> </div> </div> <div class="clearer"></div> </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="random.html" title="random — Generate pseudo-random numbers" >next</a> |</li> <li class="right" > <a href="decimal.html" title="decimal — Decimal fixed point and floating point arithmetic" >previous</a> |</li> <li><img src="../_static/py.svg" alt="Python logo" style="vertical-align: middle; 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