The problem with rounding numbers

Question

Hello. I make the algorithm of the exchange, which determines the required amount and the coefficient of 2 players based on the amount and coefficient of 1 player. The algorithm is on both JS and PHP.

var mt = { //Определяет коэф. 2 игрока findOtherRatio: function(ratioOtherPlayer){ return ratioOtherPlayer / (ratioOtherPlayer - 1) }, //Определяет прибыль 1 игрока - что также является нужной, стартовой суммой 2 игрока findProfit: function(start, ratio){ return start * ratio - start; }, //Сумма вывода игрока findOutcome: function(start, ratio){ return start * ratio; } };

Everything is considered almost true. But the problem is that in many cases the numbers look like the thousandths, millionths ... And as soon as I want to give a presentable look to the numbers, namely, a maximum of 2 digits after the decimal point, the numbers are no longer equal (1 player’s withdrawal! = 2 players’s ).

For example: imagine that 1 player put 736 rubles for 1.55

  var cof2Player = mt.findOtherRatio(1.55).toFixed(2) var money2Player = mt.findProfit(736,1.55).toFixed(2) mt.findOutcome(money2Player, cof2Player).toFixed(2) // 1141.54 mt.findOutcome(736, 1.55).toFixed(2) // 1140.80

Is there any way around this? How do different exchanges solve this? After all, they do not show the coefficients "3.8571428571428563" to players.

Accepted Answer · 2016-11-20T16:45:57

This is what will happen if you use math.js :

 var mt = { //Определяет коэф. 2 игрока findOtherRatio: function(ratioOtherPlayer){ return ratioOtherPlayer.div(ratioOtherPlayer.sub(1)); }, //Определяет прибыль 1 игрока - что также является нужной, стартовой суммой 2 игрока findProfit: function(start, ratio){ return start.mul(ratio).sub(start); }, //Сумма вывода игрока findOutcome: function(start, ratio){ return start.mul(ratio); } }; var N = math.fraction; var cof2Player = mt.findOtherRatio(N('1.55')); var money2Player = mt.findProfit(N('736'), N('1.55')); var t1 = mt.findOutcome(money2Player, cof2Player); // 1140.8 var t2 = mt.findOutcome(N('736'), N('1.55')); // 1140.8

For output you can use format :

 math.format(2.3, {notation: 'fixed', precision: 2}); // returns '2.30'

1 player has a conclusion - 1140.8; 2 players have a conclusion - 1140.7999999999997 And with toFixed () is not correct at all.
But I need to conveniently provide and store data in the database, in the format of 2 numbers after the point.
Exact calculations are a hurry to the rescue: mathjs.org/docs/datatypes/fractions.html .
Alternatively, use the modulo comparison: Если abs(xy) < 1e-5, то x == y.
It is even more important for me to turn this logic on the server using php.
@Vadim, s - sign (sign), n - numerator (numerator), d - denominator (denominator).

The problem with rounding numbers

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