首先，如果你想转换一个十进制数，你需要在转换之前知道情况的状态，假设你有0.333333，数字3是无限重复的。我们都知道 0.333333 是 1/3 。有些人认为乘以小数点后的位数会转换它。那是在某些情况下是错误的，而在其他情况下是正确的。这是与数学有关的东西。另一种情况是0.25，取小数点后的数除以100化简，等于1/4。
州已经讲完了，还有一个，但我不打算解释它，因为它很长。
但是，在数学中，我们有 3 种状态可以将十进制数转换为分数，我不打算解释它们，因为这需要大量的空间和时间，我已经为这个问题编写了一个程序。这是代码：
import java.math.BigDecimal;
import java.math.BigInteger;
public class Main {
static BigDecimal finalResult = new BigDecimal("0");
static boolean check(short[] checks) {
boolean isContinues = true;
int index = -1;
for (short ind : checks) {
index++;
if (ind==1) {
}
else if (ind==0) {
isContinues = false;
break;
}
else if (ind==-1) {
if (index==0) {
isContinues = false;
}
break;
}
}
return isContinues;
}
static int[] analyzeDecimal() { // will return int[3]
int[] analysis = new int[3];
int dot = finalResult.toString().indexOf(".");
String num = finalResult.toString();
int state = -1;
int firstPart = 0; // first part will be compared with each secondPart!
int secondPart = 0;
String part = ""; // without the dot
int index = 0; // index for every loop!
int loop = 6;
int originalLoop = loop;
int size = 0; // until six!
int ps = -1;
short[] checks = new short[] {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1}; // 10 compares for each part!
// length of checks is 10!
int continues = -1; // -1 means there is no continues part!
boolean stop = false;
while (true) { // while for size!
if (size!=6) {
while (true) { // we need to compare a part with a part!
// while for loop
// 6 loops, every loop will increase the compared part by 1!
if (loop!=-1) { // TODO : check every part with the increasing pos
firstPart = dot+1+(originalLoop-loop); // changed
try {
part = num.substring(firstPart, firstPart+(size+1));
}
catch (StringIndexOutOfBoundsException ex) {
break;
}
int partSize = part.length();
int afterDecimal = num.length()-(dot+1);
while (index!=checks.length &&
firstPart+partSize+index*partSize-(dot+1)<=afterDecimal) { // while for index!
secondPart = firstPart+partSize+index*partSize;
String comparedPart;
try {
comparedPart = num.substring(secondPart, secondPart+partSize);
}
catch (StringIndexOutOfBoundsException ex) {
break;
}
if (part.equals(comparedPart)) {
checks[index] = 1;
}
else {
checks[index] = 0;
}
index++;
}
index = 0;
if (check(checks)) {
stop = true;
continues = firstPart;
ps = partSize;
}
for (int i = 0 ; i!=10 ; i++) {
checks[i] = -1;
}
}
else { // finished!
break;
}
loop--;
if (stop) {
break;
}
}
loop = originalLoop;
size++;
if (stop) {
break;
}
}
else {
break;
}
}
if (continues==-1) {
state = 2;
}
else {
if (dot+1==continues) {
state = 1;
}
else {
state = 0;
}
}
analysis[0] = state;
analysis[1] = continues;
analysis[2] = ps;
return analysis;
}
static String convertToStandard() {
// determine the state first :
int[] analysis = analyzeDecimal();
int dot = finalResult.toString().indexOf('.')+1;
int continues = analysis[1];
int partSize = analysis[2]; // how many steps after the continues part
if (analysis[0]==0) { // constant + continues
String number = finalResult.toString().substring(0, continues+partSize);
int numOfConst = continues-dot;
int numOfDecimals = continues+partSize-dot;
int den = (int)(Math.pow(10, numOfDecimals)-Math.pow(10, numOfConst)); // (10^numOfDecimals)-(10^numOfConst);
int num;
int toSubtract = Integer.parseInt(number.substring(0, dot-1)+number.substring(dot, dot+numOfConst));
if (number.charAt(0)==0) {
num = Integer.parseInt(number.substring(dot));
}
else {
num = Integer.parseInt(number.replace(".", ""));
}
num -= toSubtract;
return simplify(num, den);
}
else if (analysis[0]==1) { // continues
int num, den;
// we always have to subtract by only one x!
String n = finalResult.toString().substring(0, dot+partSize).replace(".", "");
num = Integer.parseInt(n);
den = nines(partSize);
int toSubtract = Integer.parseInt(finalResult.toString().substring(0, dot-1));
num -= toSubtract;
return simplify(num, den);
}
else if (analysis[0]==2) { // constant
partSize = finalResult.toString().length()-dot;
int num = Integer.parseInt(finalResult.toString().replace(".", ""));
int den = (int)Math.pow(10, partSize);
return simplify(num, den);
}
else {
System.out.println("[Error] State is not determined!");
}
return "STATE NOT DETERMINED!";
}
static String simplify(int num, int den) {
BigInteger n1 = new BigInteger(Integer.toString(num));
BigInteger n2 = new BigInteger(Integer.toString(den));
BigInteger GCD = n1.gcd(n2);
String number = Integer.toString(num/GCD.intValue())+"/"+Integer.toString(den/GCD.intValue());
return number;
}
static int nines(int n) {
StringBuilder result = new StringBuilder();
while (n!=0) {
n--;
result.append("9");
}
return Integer.parseInt(result.toString());
}
public static void main(String[] args) {
finalResult = new BigDecimal("1.222222");
System.out.println(convertToStandard());
}
}
上述程序将为您提供高精度的最佳结果。您所要做的就是更改 main 函数中的 finalResult 变量。