1/x 倒数计算器（小数、分数、带分数）Reciprocal Calculator (Decimals, Fractions, Mixed Numbers)
求任意数的倒数 1/x。可以输入小数，也可以输入分数（3/4）或带分数（2 1/3），结果给出最简分数和小数形式，并验证 x × 1/x = 1。本地处理。Finds the reciprocal 1/x of any number. Enter a decimal, a fraction (3/4) or a mixed number (2 1/3) and get the result as a simplified fraction and a decimal, with the check x × 1/x = 1. Processed locally.
使用说明与常见问题How-to & FAQ
「倒数计算器（小数、分数、带分数）」是什么？What is the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) tool?
求任意数的倒数 1/x。可以输入小数，也可以输入分数（3/4）或带分数（2 1/3），结果给出最简分数和小数形式，并验证 x × 1/x = 1。本地处理。Finds the reciprocal 1/x of any number. Enter a decimal, a fraction (3/4) or a mixed number (2 1/3) and get the result as a simplified fraction and a decimal, with the check x × 1/x = 1. Processed locally.
如何使用「倒数计算器（小数、分数、带分数）」？How do I use the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) tool?
在「倒数计算器（小数、分数、带分数）」中，填写「输入形式」、「x」、「分数（如 3/4 或 2 1/3）」等参数，结果会随输入实时计算并显示在下方。In the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers): Fill in "Input form", "x", "Fraction (such as 3/4 or 2 1/3)"; results are recalculated instantly as you type.
倒数是什么？What is a reciprocal?
一个数 x 的倒数是 1/x，它们的乘积等于 1。例如 4 的倒数是 1/4 = 0.25，3/4 的倒数是 4/3。0 没有倒数。The reciprocal of x is 1/x, and the two multiply to 1. The reciprocal of 4 is 1/4 = 0.25 and of 3/4 is 4/3. Zero has no reciprocal.
带分数的倒数怎么求？How do I take the reciprocal of a mixed number?
先化成假分数再颠倒分子分母。例如 2 1/3 = 7/3，倒数是 3/7。Convert it to an improper fraction first, then flip it. 2 1/3 = 7/3, so its reciprocal is 3/7.
负数有倒数吗？Do negative numbers have reciprocals?
有，符号不变。例如 −5 的倒数是 −1/5 = −0.2。Yes, with the same sign. The reciprocal of −5 is −1/5 = −0.2.
能举个计算实例吗？Can you show a worked example?
例如在「倒数计算器（小数、分数、带分数）」中填 输入形式 = 小数 / 整数，x = 4，结果区显示：1/x：0.25；分数形式：1/4；原数分数：4；验证：4 × 0.25 ≈ 1For example, entering Input form = Decimal or whole number, x = 4 in the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) gives: 1/x: 0.25; As a fraction: 1/4; Original as a fraction: 4; Check: 4 × 0.25 ≈ 1
哪些输入会被检查？Which inputs are validated?
「倒数计算器（小数、分数、带分数）」会检查这些输入——「x」：所选方式用到时必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) checks its inputs — "x": required when the chosen option uses it; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「倒数计算器（小数、分数、带分数）」的设置：「输入形式」可选 小数 / 整数、分数或带分数（默认 小数 / 整数）；「x」默认 4；「分数（如 3/4 或 2 1/3）」默认 3/4。每次生成结果都按当前设置处理。Settings in the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) — "Input form": Decimal or whole number, Fraction or mixed number (default Decimal or whole number); "x" default 4; "Fraction (such as 3/4 or 2 1/3)" default 3/4. The result always uses the current settings.
计算精度如何？How precise are the results?
「倒数计算器（小数、分数、带分数）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「倒数计算器（小数、分数、带分数）」免费吗？需要注册吗？Is the Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) free? Do I need an account?
「倒数计算器（小数、分数、带分数）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Reciprocal Calculator (Decimals, Fractions, Mixed Numbers) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.