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BigDecimal a = new BigDecimal(1.01);
        BigDecimal b = new BigDecimal(2.02);

        BigDecimal c = new BigDecimal("1.01");
        BigDecimal d = new BigDecimal("2.02");

        BigDecimal e = new BigDecimal(Double.toString(1.01));
        BigDecimal f = new BigDecimal(Double.toString(2.02));

        BigDecimal g = BigDecimal.valueOf(1.01);
        BigDecimal h = BigDecimal.valueOf(2.02);

        System.out.println(a.add(b));
        System.out.println(c.add(d));
        System.out.println(e.add(f));
        System.out.println(g.add(h));

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3.0300000000000000266453525910037569701671600341796875
3.03
3.03
3.03

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 /**
     * Translates a {@code double} into a {@code BigDecimal} which
     * is the exact decimal representation of the {@code double}'s
     * binary floating-point value.  The scale of the returned
     * {@code BigDecimal} is the smallest value such that
     * <code>(10<sup>scale</sup> &times; val)</code> is an integer.
     * <p>
     * <b>Notes:</b>
     * <ol>
     * <li>
     * The results of this constructor can be somewhat unpredictable.
     * One might assume that writing {@code new BigDecimal(0.1)} in
     * Java creates a {@code BigDecimal} which is exactly equal to
     * 0.1 (an unscaled value of 1, with a scale of 1), but it is
     * actually equal to
     * 0.1000000000000000055511151231257827021181583404541015625.
     * This is because 0.1 cannot be represented exactly as a
     * {@code double} (or, for that matter, as a binary fraction of
     * any finite length).  Thus, the value that is being passed
     * <em>in</em> to the constructor is not exactly equal to 0.1,
     * appearances notwithstanding.
     *
     * <li>
     * The {@code String} constructor, on the other hand, is
     * perfectly predictable: writing {@code new BigDecimal("0.1")}
     * creates a {@code BigDecimal} which is <em>exactly</em> equal to
     * 0.1, as one would expect.  Therefore, it is generally
     * recommended that the {@linkplain #BigDecimal(String)
     * String constructor} be used in preference to this one.
     *
     * <li>
     * When a {@code double} must be used as a source for a
     * {@code BigDecimal}, note that this constructor provides an
     * exact conversion; it does not give the same result as
     * converting the {@code double} to a {@code String} using the
     * {@link Double#toString(double)} method and then using the
     * {@link #BigDecimal(String)} constructor.  To get that result,
     * use the {@code static} {@link #valueOf(double)} method.
     * </ol>
     *
     * @param val {@code double} value to be converted to
     *        {@code BigDecimal}.
     * @throws NumberFormatException if {@code val} is infinite or NaN.
     */
    public BigDecimal(double val) {
        this(val,MathContext.UNLIMITED);
    }

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public BigDecimal(String val) {
        this(val.toCharArray(), 0, val.length());
    }

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public static BigDecimal valueOf(double val) {
        // Reminder: a zero double returns '0.0', so we cannot fastpath
        // to use the constant ZERO.  This might be important enough to
        // justify a factory approach, a cache, or a few private
        // constants, later.
        return new BigDecimal(Double.toString(val));
    }

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@Test
public void a(){
    float a= 0.1f;
    double b = a;
    System.out.println(a);
    System.out.println(b);

    BigDecimal bigDecimal = BigDecimal.valueOf(0.1f);
    System.out.println(bigDecimal);
}

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0.1
0.10000000149011612
0.10000000149011612

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    public static void main(String[] args) {
        BigDecimal a = new BigDecimal(0.00);
        BigDecimal b = new BigDecimal(0);
 
        boolean result = a.equals(b);
        System.out.println("a equals b -->" + result);
 
        BigDecimal c = new BigDecimal("0.00");
        BigDecimal d = new BigDecimal("0");
 
        boolean result1 = c.equals(d);
        System.out.println("c equals d -->" + result1);
    }

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a equals b -->true
c equals d -->false

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boolean result2 = c.compareTo(d) == 0;
System.out.println("c compareTo d -->" + result2);

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    public BigDecimal(String val) {
        this(val.toCharArray(), 0, val.length());
    }

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* <p><b>Examples:</b><br>
     * The value of the returned {@code BigDecimal} is equal to
     * <i>significand</i> &times; 10<sup>&nbsp;<i>exponent</i></sup>.
     * For each string on the left, the resulting representation
     * [{@code BigInteger}, {@code scale}] is shown on the right.
     * <pre>
     * "0"            [0,0]
     * "0.00"         [0,2]
     * "123"          [123,0]
     * "-123"         [-123,0]
     * "1.23E3"       [123,-1]
     * "1.23E+3"      [123,-1]
     * "12.3E+7"      [123,-6]
     * "12.0"         [120,1]
     * "12.3"         [123,1]
     * "0.00123"      [123,5]
     * "-1.23E-12"    [-123,14]
     * "1234.5E-4"    [12345,5]
     * "0E+7"         [0,-7]
     * "-0"           [0,0]
     * </pre>
     *

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 @Override
    public boolean equals(Object x) {
        if (!(x instanceof BigDecimal))
            return false;
        BigDecimal xDec = (BigDecimal) x;
        if (x == this)
            return true;
        if (scale != xDec.scale)
            return false;
        long s = this.intCompact;
        long xs = xDec.intCompact;
        if (s != INFLATED) {
            if (xs == INFLATED)
                xs = compactValFor(xDec.intVal);
            return xs == s;
        } else if (xs != INFLATED)
            return xs == compactValFor(this.intVal);
 
        return this.inflated().equals(xDec.inflated());
    }

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/**
     * Compares this {@code BigDecimal} with the specified
     * {@code BigDecimal}.  Two {@code BigDecimal} objects that are
     * equal in value but have a different scale (like 2.0 and 2.00)
     * are considered equal by this method.  This method is provided
     * in preference to individual methods for each of the six boolean
     * comparison operators ({@literal <}, ==,
     * {@literal >}, {@literal >=}, !=, {@literal <=}).  The
     * suggested idiom for performing these comparisons is:
     * {@code (x.compareTo(y)} &lt;<i>op</i>&gt; {@code 0)}, where
     * &lt;<i>op</i>&gt; is one of the six comparison operators.
     *
     * @param  val {@code BigDecimal} to which this {@code BigDecimal} is
     *         to be compared.
     * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
     *          less than, equal to, or greater than {@code val}.
     */
    public int compareTo(BigDecimal val) {
        // Quick path for equal scale and non-inflated case.
        if (scale == val.scale) {
            long xs = intCompact;
            long ys = val.intCompact;
            if (xs != INFLATED && ys != INFLATED)
                return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
        }
        int xsign = this.signum();
        int ysign = val.signum();
        if (xsign != ysign)
            return (xsign > ysign) ? 1 : -1;
        if (xsign == 0)
            return 0;
        int cmp = compareMagnitude(val);
        return (xsign > 0) ? cmp : -cmp;
    }