Java在简单方程中重复十进制 [英] Java repeating decimal in simple equation

问题描述

我正在完成一项学校作业，其中我解决了一个涉及圆圈坐标的方程式（r ^ 2 = x ^ 2 + y ^ 2）r = 1，并且你通过x值递增求解y。我得到一个重复的小数，即使我只增加了十分之一。我不知道为什么，并以几种不同的方式尝试过它。这是代码。

I am doing a school assignment in which I solve an equation involving coordinates in a circle (r^2 = x^2 + y^2) were r = 1, and you increment through x values solving for y. I am getting a repeating decimals even though I only incrementing in tenths. I have no idea why and have tried it in a few different ways. Here is the code.

    double r = 1;
    double rSqr;
    double x = 1;
    double xSqr;
    double y;
    double ySqr;
    double inc = 0.1;
    int count = 0;
    while(x > -r)
    {
        x = r - (count * inc);
        rSqr = Math.pow(r, 2);
        xSqr = Math.pow(x, 2);
        ySqr = rSqr - xSqr;
        y = Math.sqrt(ySqr);
        count++;
        System.out.println(x + " " + y);
    }

输出为

1.0 0.0
0.9 0.4358898943540673
0.8 0.5999999999999999
0.7 0.714142842854285
0.6 0.8
0.5 0.8660254037844386
0.3999999999999999 0.9165151389911681
0.29999999999999993 0.9539392014169457
0.19999999999999996 0.9797958971132712
0.09999999999999998 0.99498743710662
0.0 1.0
-0.10000000000000009 0.99498743710662
-0.20000000000000018 0.9797958971132712
-0.30000000000000004 0.9539392014169457
-0.40000000000000013 0.9165151389911679
-0.5 0.8660254037844386
-0.6000000000000001 0.7999999999999999
-0.7000000000000002 0.7141428428542849
-0.8 0.5999999999999999
-0.9000000000000001 0.43588989435406705
-1.0 0.0

推荐答案

问题是 double 不精确。它使用64位来表示十进制数;一些位用于数字部分，一些用于指数，但许多看似简单的十进制数不能以这种方式准确表示，例如 0.1 。有关详情，请参见此Wiki文章。

The problem is that double is imprecise. It uses 64 bits to represent decimal numbers; some bits are used for the numeric part, and some for the exponent, but many seemingly simple decimal numbers can not be accurately represented in this way, for example 0.1. See this wiki article for more.

解决问题的一种方法是使用 DecimalFormat 显示数字，这可以将数字四舍五入以用于演示目的。下面是一些示例代码：

One way around the problem is to display the number using DecimalFormat, which can round the number for presentation purposes. Here's some example code:

public static void main(String[] args) {
    DecimalFormat decimalFormat = new DecimalFormat("#0.000");
    double d = 1 - .9; // one way to get a repeating decimal floating point number 
    System.out.println(d);
    System.out.println(decimalFormat.format(d));
}

输出：

0.09999999999999998
0.100

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