Rounding to an arbitrary number of significant digits

Here's a short and sweet JavaScript implementation:

function sigFigs(n, sig) {
    var mult = Math.pow(10, sig - Math.floor(Math.log(n) / Math.LN10) - 1);
    return Math.round(n * mult) / mult;
}

alert(sigFigs(1234567, 3)); // Gives 1230000
alert(sigFigs(0.06805, 3)); // Gives 0.0681
alert(sigFigs(5, 3)); // Gives 5

SUMMARY:

double roundit(double num, double N)
{
    double d = log10(num);
    double power;
    if (num > 0)
    {
        d = ceil(d);
        power = -(d-N);
    }
    else
    {
        d = floor(d); 
        power = -(d-N);
    }

    return (int)(num * pow(10.0, power) + 0.5) * pow(10.0, -power);
}

So you need to find the decimal place of the first non-zero digit, then save the next N-1 digits, then round the Nth digit based on the rest.

We can use log to do the first.

log 1239451 = 6.09
log 12.1257 = 1.08
log 0.0681  = -1.16

So for numbers > 0, take the ceil of the log. For numbers < 0, take the floor of the log.

Now we have the digit d: 7 in the first case, 2 in the 2nd, -2 in the 3rd.

We have to round the (d-N)th digit. Something like:

double roundedrest = num * pow(10, -(d-N));

pow(1239451, -4) = 123.9451
pow(12.1257, 1)  = 121.257
pow(0.0681, 4)   = 681

Then do the standard rounding thing:

roundedrest = (int)(roundedrest + 0.5);

And undo the pow.

roundednum = pow(roundedrest, -(power))

Where power is the power calculated above.

About accuracy: Pyrolistical's answer is indeed closer to the real result. But note that you can't represent 12.1 exactly in any case. If you print the answers as follows:

System.out.println(new BigDecimal(n));

The answers are:

Pyro's: 12.0999999999999996447286321199499070644378662109375
Mine: 12.10000000000000142108547152020037174224853515625
Printing 12.1 directly: 12.0999999999999996447286321199499070644378662109375

So, use Pyro's answer!

Isn't the "short and sweet" JavaScript implementation

Number(n).toPrecision(sig)

e.g.

alert(Number(12345).toPrecision(3)

?

Sorry, I'm not being facetious here, it's just that using the "roundit" function from Claudiu and the .toPrecision in JavaScript gives me different results but only in the rounding of the last digit.

JavaScript:

Number(8.14301).toPrecision(4) == 8.143

.NET

roundit(8.14301,4) == 8.144

Have you tried just coding it up the way you'd do it by hand?

1. Convert the number to a string
2. Starting at the beginning of the string, count digits - leading zeroes aren't significant, everything else is.
3. When you get to the "nth" digit, peek ahead at the next digit and if it's 5 or higher, round up.
4. Replace all of the trailing digits with zeroes.

I needed this in Go, which was a bit complicated by the Go standard library's lack of math.Round() (before go1.10). So I had to whip that up too. Here is my translation of Pyrolistical's excellent answer:

// TODO: replace in go1.10 with math.Round()
func round(x float64) float64 {
    return float64(int64(x + 0.5))
}

// SignificantDigits rounds a float64 to digits significant digits.
// Translated from Java at https://stackoverflow.com/a/1581007/1068283
func SignificantDigits(x float64, digits int) float64 {
    if x == 0 {
        return 0
    }

    power := digits - int(math.Ceil(math.Log10(math.Abs(x))))
    magnitude := math.Pow(10, float64(power))
    shifted := round(x * magnitude)
    return shifted / magnitude
}