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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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<div class="topic__title"><h1 class="p_Heading1"><span class="f_Heading1">Неточные вычисления в JavaScript</span></h1>
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<p class="p_Normal">in the user’s browser and in NodeJS on the server.</p>
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<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>
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<p class="p_Normal">For example, the following comparison will be defined in JavaScript as false:</p>
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<p class="p_Normal">Вычисление дробного числа в системе определяется особенностями исполнения языка JavaScript в браузере пользователя и в NodeJS на сервере.</p>
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<p class="p_Normal">В JavaScript число представлено в виде 64-битного формата IEEE-754, т. е. хранит значение с плавающей точкой, что может приводить к неточным вычислениям.</p>
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<p class="p_Normal">Например, следующее сравнение будет определено в JavaScript как ложное:</p>
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<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert( 0.1 + 0.2 == 0.3 ); </span><span class="f_CodeExample" style="font-style: italic;">// false</span></p>
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<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>
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<p class="p_Normal">Это связано с тем, что значение <span style="font-weight: bold;">0,3</span> в JavaScript вычисляется следующим образом:</p>
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<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert( 0.1 + 0.2 ); </span><span class="f_CodeExample" style="font-style: italic;">// 0.30000000000000004</span></p>
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<p class="p_Normal">This happens because a number is stored in memory as a sequence of bitsones and zeros. Fractions in such a binary system become infinite fractions.</p>
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<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>
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<p class="p_Normal">Происходит так потому, что число хранится в памяти как последовательность бит — единиц и нулей. И дроби в такой двоичной системе становятся бесконечной дробью.</p>
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<p class="p_Normal">В JavaScript не хранятся точные значения <span style="font-weight: bold;">0.1</span> или <span style="font-weight: bold;">0.2</span>. Числовой формат IEEE-754 округляет такие дроби до ближайшего возможного числа, например:</p>
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<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert( 0.1.toFixed(20) ); </span><span class="f_CodeExample" style="font-style: italic;">// 0.10000000000000000555</span></p>
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<p class="p_Normal">When we sum two fractions, their “inaccuracies” are also summed.</p>
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<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>
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<h2 class="p_Heading2"><span class="f_Heading2">Solve a fractional calculus problem</span></h2>
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<p class="p_Normal">You can try avoiding fractions altogether, or you can use the following methods.</p>
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<p class="p_Normal">Когда мы суммируем две дроби, их «неточности» тоже суммируются. </p>
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<p class="p_Normal">Отметим, что ошибка в точности вычислений для чисел с плавающей точкой сохраняется в любом языке, где используется формат IEEE-754, включая PHP, Java, C, Perl, Ruby.</p>
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<h2 class="p_Heading2"><span class="f_Heading2">Как решить проблему вычисления дробей</span></h2>
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<p class="p_Normal">Можно попробовать полностью отказаться от дробей или использовать следующие способы.</p>
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<ol style="list-style-type:upper-roman">
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<li value="1" class="p_Normal">Round the result of the calculation using the <code><b>toFixed(n)</b></code> method:</li></ol>
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<li value="1" class="p_Normal">Округлить результат вычисления с помощью метода <code><b>toFixed(n)</b></code>:</li></ol>
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<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">let sum = 0.1 + 0.2;</span><br />
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<span class="f_CodeExample">alert( sum.toFixed(2) ); </span><span class="f_CodeExample" style="font-style: italic;">// 0.30</span></p>
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<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>
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<p class="p_Normal">Метод <code><b>toFixed(n)</b></code> всегда возвращает строку, поэтому вы получите результат с заданным количеством цифр в десятичной части.</p>
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<ol style="list-style-type:upper-roman" start="2">
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<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>
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<li value="2" class="p_Normal">Временно умножить число на <span style="font-weight: bold;">100</span> (или большее), чтобы привести его к целому. Затем выполнить математические действия и разделить обратно на <span style="font-weight: bold;">100</span>. Суммируя целые числа, вы уменьшаете погрешность, но она всё равно появляется при финальном делении:</li></ol>
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<p class="p_CodeExample" style="page-break-inside: avoid;"><span class="f_CodeExample">alert( (0.1 * 10 + 0.2 * 10) / 10 ); </span><span class="f_CodeExample" style="font-style: italic;">// 0.3</span><br />
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<span class="f_CodeExample">alert( (0.28 * 100 + 0.14 * 100) / 100); </span><span class="f_CodeExample" style="font-style: italic;">// 0.4200000000000001</span></p>
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<p class="p_Normal">Thus, the multiplication and division methods reduce the error but does not completely solve it.</p>
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<p class="p_Normal">Таким образом, метод умножения и деления уменьшает погрешность, но полностью не решает её.</p>
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<div class="footer-mobile">
|
||||
|
||||
<ul class="footer-mobile__list"><li><a href="https://brix365.com/en/" target="_blank">BRIX</a></li><li><a href="https://tssdk.brix365.com/en/latest/" target="_blank">SDK</a></li><li><a href="https://api.brix365.com/en/" target="_blank">API</a></li></ul><ul class="footer-mobile__list"><li><a href="https://brix365.com/en/help/platform/get-trial.html">Platform</a></li><li><a href="https://brix365.com/en/help/ecm/ecm-functions.html">ECM</a></li><li><a href="https://brix365.com/en/help/service/service-functions.html">Service</a></li><li><a href="https://brix365.com/en/help/projects/projects-functions.html">Projects</a></li></ul>
|
||||
<ul class="footer-mobile__list"><li><a href="https://api.elma365.com/ru/" target="_blank">API</a></li><li><a href="https://tssdk.elma365.com/" target="_blank">TS SDK</a></li><li><a href="https://community.elma365.com/" target="_blank">Community</a></li><li><a href="https://elma-academy.com/ru/elma365" target="_blank">Академия</a></li></ul><ul class="footer-mobile__list"><li><a href="https://elma365.com/ru/help/platform/get-trial.html">Платформа</a></li><li><a href="https://elma365.com/ru/help/ecm/ecm-functions.html">ECM</a></li><li><a href="https://elma365.com/ru/help/service/service-functions.html">Service</a></li><li><a href="https://elma365.com/ru/help/projects/projects-functions.html">Проекты</a></li></ul>
|
||||
|
||||
|
||||
</div>
|
||||
<div class="footer-wrap">
|
||||
|
||||
<div><span class="mobile-question-popup">Send feedback</span><form method="POST" action class="question__popup question-xs" id="question__popup"><div class="question-wrap"><span class="close"></span><span class="title">Ask a question</span><label for="help_question" style="display: none;"></label><textarea name="help_question" id="help_question"></textarea><input type="submit" value="Send"></div></form><div class="hidden fade-in question-success-xs">Sent</div></div>
|
||||
|
||||
<div class="footer-flex-b">
|
||||
<span class="footer-copy">© 2025 BRIX</span>
|
||||
<ul class="footer-list">
|
||||
|
||||
<li class="footer-item">
|
||||
<a href="#" class="arrow-top" style="display: block;"></a>
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
<div class="container">
|
||||
<div class="footer-wrap">
|
||||
|
||||
<div><span class="mobile-question-popup">Отправить фидбэк</span><form method="POST" action class="question__popup question-xs" id="question__popup"><div class="question-wrap"><span class="close"></span><span class="title">Задать вопрос</span><label for="help_question" style="display: none;"></label><textarea name="help_question" id="help_question"></textarea><input type="submit" value="Отправить"></div></form><div class="hidden fade-in question-success-xs">Ваш фидбэк отправлен.</div></div>
|
||||
|
||||
<div class="footer-flex-b">
|
||||
<div class="footer-top">
|
||||
<span class="footer-copy">© 2025
|
||||
ELMA365
|
||||
|
||||
|
||||
</span>
|
||||
|
||||
<a href="https://navigator.sk.ru/orn/1122971" target="_blank">
|
||||
<img src="sk-resident.svg" alt="sk icon" class="footer-img" width="117" height="34">
|
||||
</a>
|
||||
|
||||
</div>
|
||||
<div class="footer-line">
|
||||
|
||||
<div class="footer-line-copy">
|
||||
<span class="footer-copy">© 2025
|
||||
ELMA365
|
||||
|
||||
|
||||
</span>
|
||||
</div>
|
||||
|
||||
<ul class="footer-list">
|
||||
|
||||
<li class="footer-item"><a href="https://elma365.com/ru/" target="_blank" class="footer-link" style="color: #0D4A75;"><img src="browse.svg" alt="browse icon" class="footer-img">elma365.com</a></li><li class="footer-item"><a href="https://www.youtube.com/user/ELMABPM" target="_blank" class="footer-link"><img src="yt.svg" alt="youtube icon" class="footer-img"></a></li><li class="footer-item"><a href="https://vk.com/elma_bpm" target="_blank" class="footer-link"><img src="vk.svg" alt="vk icon" class="footer-img"></a></li><li class="footer-item"><a href="https://t.me/elmaday" target="_blank" class="footer-link"><img src="tg.svg" alt="telegram icon" class="footer-img"></a></li><li class="footer-item"><a href="https://dzen.ru/elma" target="_blank" class="footer-link"><img src="dzen.svg" alt="dzen icon" class="footer-img"></a></li>
|
||||
|
||||
|
||||
<li class="footer-item">
|
||||
<a href="https://navigator.sk.ru/orn/1122971" target="_blank">
|
||||
<img src="sk-resident.svg" alt="sk icon" class="footer-img" width="117" height="34">
|
||||
</a>
|
||||
</li>
|
||||
|
||||
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<a href="#" class="arrow-top"></a>
|
||||
</div>
|
||||
|
||||
</footer>
|
||||
<!-- <script type="text/javascript" src="jquery1.min.js"></script>-->
|
||||
<iframe name="hmnavigation" style="display:none!important"></iframe>
|
||||
<script src="./jquery-ui.js"></script>
|
||||
<!--<script src="./jquery-ui.js"></script> -->
|
||||
<script src="./jquery-ui.min.js"></script>
|
||||
<!--script src="//cdn.jsdelivr.net/npm/featherlight@1.7.14/release/featherlight.min.js" type="text/javascript" charset="utf-8"></script-->
|
||||
<script src="./jquery.tocify.min.js"></script>
|
||||
<script src="./TypoReporter.min.js"></script>
|
||||
|
||||
Reference in New Issue
Block a user