math help

> why isn't it 1890

Some numbers that can be represented exactly in base-10 cannot be represented exactly in base-2.

For example, one-tenth in base-10 is 0.1

In base-2, you cannot represent this number exactly. It is a repeating fraction, just like one-third is in base-10.

0.1 = 1/2

0.01 = 1/4

etc.

Try to get those negative powers of 2 to add up to exactly one-tenth. You can't do it.

There are uncountably infinitely many numbers in the range covered by double, but only a finite number of bits with which to represent them. Many of them (uncountably infinitely many) cannot be represented exactly, so an approximation will be used.

> and how can I get 1890?

Use java.text.DecimalFormat to format the output, or use java.math.BigDecimal.

jverda at 2007-7-14 20:47:09 >

The input and output numerals are based on the base or radix 10 (decimal system).

1 * 10`1 + 8*10`0 + 9*10`-1 = 18.9

But the computer uses for the numerals the binary system base on the base 2.

1*2`4 + 0*2`3 + 0*2`2 +1*2`1 + 0*2`0 + 1*2`-1+1*2`-2+1*2`-3+0*2`-3+......

The problem are the transformations from the decimal to the binary system and reverse. In both cases a limited number of bytes is used. Therefore you get the differences.

Using BigDecimal delivers precise results, because they use a BCD (binary coded decimals) representation.

public static void main(String[] args) {

double factor1 = 18.9;

double factor2 = 100;

double result = factor1 * factor2;

System.out.println(" 18.9 * 100 = " + result);

BigDecimal bdFactor1 = new BigDecimal("18.9");

BigDecimal bdFactor2 = new BigDecimal("100");

System.out.println(" 18.9 * 100 = " + bdFactor1.multiply(bdFactor2));

}

Result:

18.9 * 100 = 1889.9999999999998

18.9 * 100 = 1890.0

D_Daniela at 2007-7-14 20:47:09 >

I am doing:

BigDecimal bdfirst = new BigDecimal(first);

BigDecimal bdsecond= new BigDecimal(second);

BigDecimal bdtrunc = bdfirst.multiply(bdsecond);

System.out.println(first+" * "+second+" = "+bdtrunc.toString());

my result is:

747.5 * 0.09 = 67.27499999999999751032486727808645810000598430633544921875

the answer should be 67.275 - why am I getting this imprecise value still?

celfiea at 2007-7-14 20:47:09 >

ok here is the problem

System.out.println(bdfirst.toString()+" * "+bdsecond.toString()+" = "+bdfirst.multiply(bdsecond));

747.5 * 0.0899999999999999966693309261245303787291049957275390625 = 67.27499999999999751032486727808645810000598430633544921875

So when i create my big decimal objects and pass the constuctor the double as argument, the real number is stored imprecisely mucking up my calculation. Is the solution to convert my doubles to strings before creating the bigdecimal? i can't possibly store all these values as strings - it would require a overhaul of my whole application. any tips?

celfiea at 2007-7-14 20:47:09 >

> last question i promise

>

> if I take my double and do a new double().toString()

> will this be effective for all cases or should i just

> retrieve my values as strings directly from the DB

I don't see what you can hope to achieve with this. It probably won't work because once you place a value in a double the damge is done.

Use double and DecimalFormat.

sabre150a at 2007-7-14 20:47:09 >