Round a double to 3 significant figures

double d = ...;
BigDecimal bd = new BigDecimal(d);
bd = bd.round(new MathContext(3));
double rounded = bd.doubleValue();

If you want to do it by hand:

import java.lang.Math;

public class SigDig {

  public static void main(String[] args) {
    System.out.println("   -123.456   rounded up   to 2 sig figures is " + sigDigRounder(-123.456, 2,  1));
    System.out.println("     -0.03394 rounded down to 3 sig figures is " + sigDigRounder(-0.03394, 3, -1));
    System.out.println("    474       rounded up   to 2 sig figures is " + sigDigRounder(474, 2,  1));
    System.out.println("3004001       rounded down to 4 sig figures is " + sigDigRounder(3004001, 4, -1));
  }

  public static double sigDigRounder(double value, int nSigDig, int dir) {

    double intermediate = value/Math.pow(10,Math.floor(Math.log10(Math.abs(value)))-(nSigDig-1));

    if(dir > 0)      intermediate = Math.ceil(intermediate);
    else if (dir< 0) intermediate = Math.floor(intermediate);
    else             intermediate = Math.round(intermediate);

    double result = intermediate * Math.pow(10,Math.floor(Math.log10(Math.abs(value)))-(nSigDig-1));

    return(result);

  }
}

The above method rounds a double to a desired number of significant figures, handles negative numbers, and can be explicitly told to round up or down

There's nothing wrong with the answer given by Sean Owen (https://stackoverflow.com/a/7548871/274677). However depending on your use case you might want to arrive at a String representation. In that case, IMO it is best to convert while still in BigDecimal space using:

bd.toPlainString();

... if that's your use case then you might be frustrated that the code adapted from Owen's answer will produce the following:

d = 0.99, significantDigits = 3 ==> 0.99

... instead of the strictly more accurate 0.990.

If such things are important in your use case then I suggest the following adaptation to Owen's answer ; you can obviously also return the BigDecimal itself instead of calling toPlainString() — I just provide it this way for completeness.

public static String setSignificanDigits(double value, int significantDigits) {
    if (significantDigits < 0) throw new IllegalArgumentException();

    // this is more precise than simply doing "new BigDecimal(value);"
    BigDecimal bd = new BigDecimal(value, MathContext.DECIMAL64);
    bd = bd.round(new MathContext(significantDigits, RoundingMode.HALF_UP));
    final int precision = bd.precision();
    if (precision < significantDigits)
    bd = bd.setScale(bd.scale() + (significantDigits-precision));
    return bd.toPlainString();
}