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Number.prototype.decToBase = function(base) {

  const EPSILON = 1e-7,
        MAXD = 50;

  const digits = ["0","1","2","3","4","5","6","7","8","9",
    "a","b","c","d","e","f","g","h","i","j","k","l","m",
    "n","o","p","q","r","s","t","u","v","w","x","y","z"];

  function posIntTo(i, base) {
    let num = "";
    while (i > 0) {
      num = digits[i % base] + num;
      i = Math.floor(i/base);
    }
    return num;
  }

  function posFrcTo(f, base) {
    let num = "";
    for (let d = 0; f > EPSILON && d < MAXD; d++) {
      let p = f * base;
      num += digits[Math.floor(p)];
      f = p % 1;
    }
    return num;
  }

  const
    decNum = this,
    posN = Math.abs(decNum),
    posI = Math.floor(posN),
    posF = posN - posI,
    newI = posI > 0 ? posIntTo(posI, base) : "0",
    newF = posF > 0 ? posFrcTo(posF, base) : "0",
    newN = newF !== "0" ? newI + "." + newF : newI,
    num = decNum < 0 ? "-" + newN : newN;

  return num;
}

String.prototype.decFromBase = function(base) {

  const digits = {0:0,1:1,2:2,3:3,4:4,5:5,6:6,7:7,8:8,9:9,
    a:10,b:11,c:12,d:13,e:14,f:15,g:16,h:17,i:18,j:19,k:20,
    l:21,m:22,n:23,o:24,p:25,q:26,r:27,s:28,t:29,u:30,v:31,
    w:32,x:33,y:34,z:35};

  function validate(str, b) {
    if (b < 2 || b > 36) {
      throw Error(b + " is an invalid base.");
    }
    str = str.toLowerCase();
    for (let i = str.length - 1; i >= 0; i--) {
      let decVal = digits[str[i]];
      if (!(decVal <  b)) {
        throw Error("Invalid base " + b + " number.");
      }
    }
    return str;
  }

  function digitsToDec(strI, strF, b) {

    const strN = validate(strI + strF, b);

    let
      p = 1 / Math.pow(b, strF.length),
      numD = 0;

    for (let i = strN.length - 1; i >= 0; i--) {
      numD += digits[strN[i]] * p;
      p *= b;
    }

    return numD;
  }

  const
    num = this,
    isNeg = num[0] === "-",
    posN = isNeg ? num.slice(1) : num,
    parts = num.split("."),
    posI = parts[0],
    posF = parts.length === 2 ? parts[1] : "",
    decN = digitsToDec(posI, posF, base),
    decNum = num < 0 ? "-" + decN : decN;

  return decNum;
  
}

function decToBase(decNum, base) {
  return parseFloat(decNum).decToBase(base);
}

String.prototype.decToBase = function(base) {
  return decToBase(this, base);
}

function decFromBase(num, base) {
  return num.toString().decFromBase(base);
}

Number.prototype.decFromBase = function(base) {
  return decFromBase(this, base);
}
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