Round a double to x significant figures

If I have a double (234.004223), etc., I would like to round this to x significant digits in C#.

So far I can only find ways to round to x decimal places, but this simply removes the precision if there are any 0s in the number.

For example, 0.086 to one decimal place becomes 0.1, but I would like it to stay at 0.08.

The framework doesn't have a built-in function to round (or truncate, as in your example) to a number of significant digits. One way you can do this, though, is to scale your number so that your first significant digit is right after the decimal point, round (or truncate), then scale back. The following code should do the trick:

static double RoundToSignificantDigits(this double d, int digits){
    if(d == 0)
        return 0;

    double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
    return scale * Math.Round(d / scale, digits);
}

If, as in your example, you really want to truncate, then you want:

static double TruncateToSignificantDigits(this double d, int digits){
    if(d == 0)
        return 0;

    double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1 - digits);
    return scale * Math.Truncate(d / scale);
}

I've been using pDaddy's sigfig function for a few months and found a bug in it. You cannot take the Log of a negative number, so if d is negative the results is NaN.

The following corrects the bug:

public static double SetSigFigs(double d, int digits)
{   
    if(d == 0)
        return 0;

    decimal scale = (decimal)Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
       
    return (double) (scale * Math.Round((decimal)d / scale, digits));
}

It sounds to me like you don't want to round to x decimal places at all - you want to round to x significant digits. So in your example, you want to round 0.086 to one significant digit, not one decimal place.

Now, using a double and rounding to a number of significant digits is problematic to start with, due to the way doubles are stored. For instance, you could round 0.12 to something close to 0.1, but 0.1 isn't exactly representable as a double. Are you sure you shouldn't actually be using a decimal? Alternatively, is this actually for display purposes? If it's for display purposes, I suspect you should actually convert the double directly to a string with the relevant number of significant digits.

If you can answer those points, I can try to come up with some appropriate code. Awful as it sounds, converting to a number of significant digits as a string by converting the number to a "full" string and then finding the first significant digit (and then taking appropriate rounding action after that) may well be the best way to go.

If it is for display purposes (as you state in the comment to Jon Skeet's answer), you should use Gn format specifier. Where n is the number of significant digits - exactly what you are after.

Here is the the example of usage if you want 3 significant digits (printed output is in the comment of each line):

    Console.WriteLine(1.2345e-10.ToString("G3"));//1.23E-10
    Console.WriteLine(1.2345e-5.ToString("G3")); //1.23E-05
    Console.WriteLine(1.2345e-4.ToString("G3")); //0.000123
    Console.WriteLine(1.2345e-3.ToString("G3")); //0.00123
    Console.WriteLine(1.2345e-2.ToString("G3")); //0.0123
    Console.WriteLine(1.2345e-1.ToString("G3")); //0.123
    Console.WriteLine(1.2345e2.ToString("G3"));  //123
    Console.WriteLine(1.2345e3.ToString("G3"));  //1.23E+03
    Console.WriteLine(1.2345e4.ToString("G3"));  //1.23E+04
    Console.WriteLine(1.2345e5.ToString("G3"));  //1.23E+05
    Console.WriteLine(1.2345e10.ToString("G3")); //1.23E+10

I found two bugs in the methods of P Daddy and Eric. This solves for example the precision error that was presented by Andrew Hancox in this Q&A. There was also a problem with round directions. 1050 with two significant figures isn't 1000.0, it's 1100.0. The rounding was fixed with MidpointRounding.AwayFromZero.

static void Main(string[] args) {
  double x = RoundToSignificantDigits(1050, 2); // Old = 1000.0, New = 1100.0
  double y = RoundToSignificantDigits(5084611353.0, 4); // Old = 5084999999.999999, New = 5085000000.0
  double z = RoundToSignificantDigits(50.846, 4); // Old = 50.849999999999994, New =  50.85
}

static double RoundToSignificantDigits(double d, int digits) {
  if (d == 0.0) {
    return 0.0;
  }
  else {
    double leftSideNumbers = Math.Floor(Math.Log10(Math.Abs(d))) + 1;
    double scale = Math.Pow(10, leftSideNumbers);
    double result = scale * Math.Round(d / scale, digits, MidpointRounding.AwayFromZero);

    // Clean possible precision error.
    if ((int)leftSideNumbers >= digits) {
      return Math.Round(result, 0, MidpointRounding.AwayFromZero);
    }
    else {
      return Math.Round(result, digits - (int)leftSideNumbers, MidpointRounding.AwayFromZero);
    }
  }
}

As Jon Skeet mentions: better handle this in the textual domain. As a rule: for display purposes, don't try to round / change your floating point values, it never quite works 100%. Display is a secondary concern and you should handle any special formatting requirements like these working with strings.

My solution below I implemented several years ago and has proven very reliable. It has been thoroughly tested and it performs quite well also. About 5 times longer in execution time than P Daddy / Eric's solution.

Examples of input + output given below in code.

using System;
using System.Text;

namespace KZ.SigDig
{
    public static class SignificantDigits
    {
        public static string DecimalSeparator;

        static SignificantDigits()
        {
            System.Globalization.CultureInfo ci = System.Threading.Thread.CurrentThread.CurrentCulture;
            DecimalSeparator = ci.NumberFormat.NumberDecimalSeparator;
        }

        /// <summary>
        /// Format a double to a given number of significant digits.
        /// </summary>
        /// <example>
        /// 0.086 -> "0.09" (digits = 1)
        /// 0.00030908 -> "0.00031" (digits = 2)
        /// 1239451.0 -> "1240000" (digits = 3)
        /// 5084611353.0 -> "5085000000" (digits = 4)
        /// 0.00000000000000000846113537656557 -> "0.00000000000000000846114" (digits = 6)
        /// 50.8437 -> "50.84" (digits = 4)
        /// 50.846 -> "50.85" (digits = 4)
        /// 990.0 -> "1000" (digits = 1)
        /// -5488.0 -> "-5000" (digits = 1)
        /// -990.0 -> "-1000" (digits = 1)
        /// 0.0000789 -> "0.000079" (digits = 2)
        /// </example>
        public static string Format(double number, int digits, bool showTrailingZeros = true, bool alwaysShowDecimalSeparator = false)
        {
            if (Double.IsNaN(number) ||
                Double.IsInfinity(number))
            {
                return number.ToString();
            }

            string sSign = "";
            string sBefore = "0"; // Before the decimal separator
            string sAfter = ""; // After the decimal separator

            if (number != 0d)
            {
                if (digits < 1)
                {
                    throw new ArgumentException("The digits parameter must be greater than zero.");
                }

                if (number < 0d)
                {
                    sSign = "-";
                    number = Math.Abs(number);
                }

                // Use scientific formatting as an intermediate step
                string sFormatString = "{0:" + new String('#', digits) + "E0}";
                string sScientific = String.Format(sFormatString, number);

                string sSignificand = sScientific.Substring(0, digits);
                int exponent = Int32.Parse(sScientific.Substring(digits + 1));
                // (the significand now already contains the requested number of digits with no decimal separator in it)

                StringBuilder sFractionalBreakup = new StringBuilder(sSignificand);

                if (!showTrailingZeros)
                {
                    while (sFractionalBreakup[sFractionalBreakup.Length - 1] == '0')
                    {
                        sFractionalBreakup.Length--;
                        exponent++;
                    }
                }

                // Place decimal separator (insert zeros if necessary)

                int separatorPosition = 0;

                if ((sFractionalBreakup.Length + exponent) < 1)
                {
                    sFractionalBreakup.Insert(0, "0", 1 - sFractionalBreakup.Length - exponent);
                    separatorPosition = 1;
                }
                else if (exponent > 0)
                {
                    sFractionalBreakup.Append('0', exponent);
                    separatorPosition = sFractionalBreakup.Length;
                }
                else
                {
                    separatorPosition = sFractionalBreakup.Length + exponent;
                }

                sBefore = sFractionalBreakup.ToString();

                if (separatorPosition < sBefore.Length)
                {
                    sAfter = sBefore.Substring(separatorPosition);
                    sBefore = sBefore.Remove(separatorPosition);
                }
            }

            string sReturnValue = sSign + sBefore;

            if (sAfter == "")
            {
                if (alwaysShowDecimalSeparator)
                {
                    sReturnValue += DecimalSeparator + "0";
                }
            }
            else
            {
                sReturnValue += DecimalSeparator + sAfter;
            }

            return sReturnValue;
        }
    }
}

Math.Round() on doubles is flawed (see Notes to Callers in its documentation). The later step of multiplying the rounded number back up by its decimal exponent will introduce further floating point errors in the trailing digits. Using another Round() as @Rowanto does won't reliably help and suffers from other problems. However if you're willing to go via decimal then Math.Round() is reliable, as is multiplying and dividing by powers of 10:

static ClassName()
{
    powersOf10 = new decimal[28 + 1 + 28];
    powersOf10[28] = 1;
    decimal pup = 1, pdown = 1;
    for (int i = 1; i < 29; i++) {
        pup *= 10;
        powersOf10[i + 28] = pup;
        pdown /= 10;
        powersOf10[28 - i] = pdown;
    }
}

/// <summary>Powers of 10 indexed by power+28.  These are all the powers
/// of 10 that can be represented using decimal.</summary>
static decimal[] powersOf10;

static double RoundToSignificantDigits(double v, int digits)
{
    if (v == 0.0 || Double.IsNaN(v) || Double.IsInfinity(v)) {
        return v;
    } else {
        int decimal_exponent = (int)Math.Floor(Math.Log10(Math.Abs(v))) + 1;
        if (decimal_exponent < -28 + digits || decimal_exponent > 28 - digits) {
            // Decimals won't help outside their range of representation.
            // Insert flawed Double solutions here if you like.
            return v;
        } else {
            decimal d = (decimal)v;
            decimal scale = powersOf10[decimal_exponent + 28];
            return (double)(scale * Math.Round(d / scale, digits, MidpointRounding.AwayFromZero));
        }
    }
}

I agree with the spirit of Jon's assessment:

> Awful as it sounds, converting to a number of significant digits as a string by converting the number to a "full" string and then finding the first significant digit (and then taking appropriate rounding action after that) may well be the best way to go.

I needed significant-digit rounding for approximate and non-performance-critical computational purposes, and the format-parse round-trip through "G" format is good enough:

public static double RoundToSignificantDigits(this double value, int numberOfSignificantDigits)
{
    return double.Parse(value.ToString("G" + numberOfSignificantDigits));
}

This question is similiar to the one you're asking:

https://stackoverflow.com/questions/158172/formatting-numbers-with-significant-figures-in-c#158942

Thus you could do the following:

double Input2 = 234.004223;
string Result2 = Math.Floor(Input2) + Convert.ToDouble(String.Format("{0:G1}", Input2 - Math.Floor(Input2))).ToString("R6");

Rounded to 1 significant digit.

Let inputNumber be input that needs to be converted with significantDigitsRequired after decimal point, then significantDigitsResult is the answer to the following pseudo code.

integerPortion = Math.truncate(**inputNumber**)

decimalPortion = myNumber-IntegerPortion

if( decimalPortion <> 0 )
{

 significantDigitsStartFrom = Math.Ceil(-log10(decimalPortion))

 scaleRequiredForTruncation= Math.Pow(10,significantDigitsStartFrom-1+**significantDigitsRequired**)

**siginficantDigitsResult** = integerPortion + ( Math.Truncate (decimalPortion*scaleRequiredForTruncation))/scaleRequiredForTruncation

}
else
{

  **siginficantDigitsResult** = integerPortion

}

As pointed out by @Oliver Bock is that Math.Round() on doubles is flawed (see Notes to Callers in its documentation). The later step of multiplying the rounded number back up by its decimal exponent will introduce further floating point errors in the trailing digits. Generally, any multiplication by or division by a power of ten gives a non-exact result, since floating-point is typically represented in binary, not in decimal.

Using the following function will avoid floating point errors in the trailing digits:

static double RoundToSignificantDigits(double d, int digits)
{
	if (d == 0.0 || Double.IsNaN(d) || Double.IsInfinity(d))
	{
		return d;
	}
	// Compute shift of the decimal point.
	int shift = digits - 1 - (int)Math.Floor(Math.Log10(Math.Abs(d)));

	// Return if rounding to the same or higher precision.
	int decimalPlaces = 0;
	for (long pow = 1; Math.Floor(d * pow) != (d * pow); pow *= 10) decimalPlaces++;
	if (shift >= decimalPlaces)
		return d;

	// Round to sf-1 fractional digits of normalized mantissa x.dddd
	double scale = Math.Pow(10, Math.Abs(shift));
	return shift > 0 ?
	       Math.Round(d * scale, MidpointRounding.AwayFromZero) / scale :
	       Math.Round(d / scale, MidpointRounding.AwayFromZero) * scale;
}

However if you're willing to go via decimal then Math.Round() is reliable, as is multiplying and dividing by powers of 10:

static double RoundToSignificantDigits(double d, int digits)
{
	if (d == 0.0 || Double.IsNaN(d) || Double.IsInfinity(d))
	{
		return d;
	}
	decimal scale = (decimal)Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
	return (double)(scale * Math.Round((decimal)d / scale, digits, MidpointRounding.AwayFromZero));
}

Console.WriteLine("{0:G17}", RoundToSignificantDigits(5.015 * 100, 15)); // 501.5

for me, this one works pretty fine and is also valid for negative numbers:

public static double RoundToSignificantDigits(double number, int digits)
{
    int sign = Math.Sign(number);

    if (sign < 0)
        number *= -1;

    if (number == 0)
        return 0;

    double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(number))) + 1);
    return sign * scale * Math.Round(number / scale, digits);
}

My solution may be helpful in some cases, I use it to display crypto prices which vary greatly in magnitude - it always gives me a specified number of significant figures but unlike ToString("G[number of digits]") it doesn't show small values in scientific notation (don't know a way to avoid this with ToString(), if there is then please let me know!)

    const int MIN_SIG_FIGS = 6; //will be one more for < 0
    int numZeros = (int)Math.Floor(Math.Log10(Math.Abs(price))); //get number of zeros before first digit, will be negative for price > 0
    int decPlaces = numZeros < MIN_SIG_FIGS
                  ? MIN_SIG_FIGS - numZeros < 0 
                        ? 0 
                        : MIN_SIG_FIGS - numZeros 
                  : 0; //dec. places: set to MIN_SIG_FIGS + number of zeros, unless numZeros greater than sig figs then no decimal places
    return price.ToString($"F{decPlaces}");

I just did:

int integer1 = Math.Round(double you want to round, 
    significant figures you want to round to)

Here is something I did in C++

/*
    I had this same problem I was writing a design sheet and
    the standard values were rounded. So not to give my
    values an advantage in a later comparison I need the
    number rounded, so I wrote this bit of code.

    It will round any double to a given number of significant
    figures. But I have a limited range written into the
    subroutine. This is to save time as my numbers were not
    very large or very small. But you can easily change that
    to the full double range, but it will take more time.

    Ross Mckinstray
    [email protected]
*/

#include <iostream>
#include <fstream>
#include <string>
#include <math.h>
#include <cmath>
#include <iomanip>

#using namespace std;

double round_off(double input, int places) {
    double roundA;
    double range = pow(10, 10); // This limits the range of the rounder to 10/10^10 - 10*10^10 if you want more change range;
    for (double j = 10/range; j< 10*range;) {
        if (input >= j && input < j*10){
            double figures = pow(10, places)/10;
            roundA = roundf(input/(j/figures))*(j/figures);
        }
        j = j*10;
    }
    cout << "\n in sub after loop";
    if (input <= 10/(10*10) && input >= 10*10) {
        roundA = input;
        cout << "\nDID NOT ROUND change range";
    }
    return roundA;
}

int main() {
    double number, sig_fig;

    do {
        cout << "\nEnter number ";
        cin >> number;
        cout << "\nEnter sig_fig ";
        cin >> sig_fig;
        double output = round_off(number, sig_fig);

        cout << setprecision(10);
        cout << "\n I= " << number;
        cout << "\n r= " <<output;
        cout << "\nEnter 0 as number to exit loop";
    }
    while (number != 0);

    return 0;
}

Hopefully I did not change anything formatting it.