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<div class="topic__title"><h1 class="p_Heading1"><span class="f_Heading1">Inaccurate calculations in JavaScript</span></h1>
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<p class="p_Normal">in the users browser and in NodeJS on the server.</p>
<p class="p_Normal">In JavaScript, a number is represented in a 64-bit IEEE-754 format, i.e., it stores a floating-point value, which can lead to inaccurate calculations.</p>
<p class="p_Normal">For example, the following comparison will be defined in JavaScript as false:</p>
<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert(&nbsp;0.1&nbsp;+&nbsp;0.2&nbsp;==&nbsp;0.3&nbsp;);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;false</span></p>
<p class="p_Normal">This is because the value of <span style="font-weight: bold;">0.3</span> in JavaScript is calculated as follows:</p>
<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert(&nbsp;0.1&nbsp;+&nbsp;0.2&nbsp;);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;0.30000000000000004</span></p>
<p class="p_Normal">This happens because a number is stored in memory as a sequence of bitsones and zeros. Fractions in such a binary system become infinite fractions.</p>
<p class="p_Normal">JavaScript does not store exact values of <span style="font-weight: bold;">0.1</span> or <span style="font-weight: bold;">0.2</span>. The IEEE-754 number format rounds such fractions to the nearest possible number, for example:</p>
<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert(&nbsp;0.1.toFixed(20)&nbsp;);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;0.10000000000000000555</span></p>
<p class="p_Normal">When we sum two fractions, their “inaccuracies” are also summed.</p>
<p class="p_Normal">Please note, that the inaccuracy in precision for floating-point numbers is retained in any language that uses IEEE-754 format, including PHP, Java, C, Perl, and Ruby.</p>
<h2 class="p_Heading2"><span class="f_Heading2">Solve a fractional calculus problem</span></h2>
<p class="p_Normal">You can try avoiding fractions altogether, or you can use the following methods.</p>
<ol style="list-style-type:upper-roman">
<li value="1" class="p_Normal">Round the result of the calculation using the <code><b>toFixed(n)</b></code> method:</li></ol>
<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">let&nbsp;sum&nbsp;=&nbsp;0.1&nbsp;+&nbsp;0.2;</span><br />
<span class="f_CodeExample">alert(&nbsp;sum.toFixed(2)&nbsp;);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;0.30</span></p>
<p class="p_Normal">The <code><b>toFixed(n)</b></code> method always returns a string, so you will get a result with the given number of digits in the decimal part.</p>
<ol style="list-style-type:upper-roman" start="2">
<li value="2" class="p_Normal">Temporarily multiply a number by <span style="font-weight: bold;">100</span> (or greater) to bring it to an integer. Then do the math and divide back by <span style="font-weight: bold;">100</span>. Summing integers reduces the inaccuracy, but it still appears in the final division:</li></ol>
<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert(&nbsp;(0.1&nbsp;*&nbsp;10&nbsp;+&nbsp;0.2&nbsp;*&nbsp;10)&nbsp;/&nbsp;10&nbsp;);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;0.3</span><br />
<span class="f_CodeExample">alert(&nbsp;(0.28&nbsp;*&nbsp;100&nbsp;+&nbsp;0.14&nbsp;*&nbsp;100)&nbsp;/&nbsp;100);&nbsp;</span><span class="f_CodeExample" style="font-style: italic;">//&nbsp;0.4200000000000001</span></p>
<p class="p_Normal">Thus, the multiplication and division methods reduce the error but does not completely solve it.</p>
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