# Multiplication Issue when Variables as Double Datatype

N.Senthil Kumar

Ranch Hand

Posts: 50

posted 6 years ago

- 0

package test1;

public class TestApp {

public static void main(String[] args) {

double a = 0.43;

double b = 0.1;

System.out.println(a * b);

}

}

The Output shows 0.043000000000000003.

But the 0.43 * 0.1 is 0.043.

May i know why the Value have 3 at last in the Output ----> 0.04300000000000000

Thanks in Advance.

public class TestApp {

public static void main(String[] args) {

double a = 0.43;

double b = 0.1;

System.out.println(a * b);

}

}

The Output shows 0.043000000000000003.

But the 0.43 * 0.1 is 0.043.

May i know why the Value have 3 at last in the Output ----> 0.04300000000000000

**3**.Thanks in Advance.

N.Senthil Kumar

Embla Tingeling

Ranch Hand

Posts: 237

posted 6 years ago

Not every decimal number (which humans prefer) can be exactly converted to a binary number (which computers prefer). So conversions back and forth between number systems tend to produce small errors.

Also the number of bits used to represent numbers internally in the computer is fixed. As you probably know a float uses 32 bits and a double 64. This means that when arithmetical operations are performed, the result may not be exact. So operations on numbers in fixed-size representation also tend to introduce small errors.

The result is what you see in your example. The combination of conversion errors and fixed-size arithmetic errors show up as a "ripple" in the result.

These kinds of errors are fundamental to digital computers so they will always be present. One way to handle them is to round the result of a calculation. As you can see the error is far smaller than the 2 digits of precision you've used in the input numbers. If you round the output to the same precision the error disappears and the result is "correct".

Also note that programmers must watch out so formulas they use don't magnify those small fundamental and unavoidable errors. Such formulas are called ill-conditioned and there's a whole branch of math called numerical mathematics which is dealing with that.

- 0

N.Senthil Kumar wrote:May i know why the Value have 3 at last in the Output ----> 0.043000000000000003.

Not every decimal number (which humans prefer) can be exactly converted to a binary number (which computers prefer). So conversions back and forth between number systems tend to produce small errors.

Also the number of bits used to represent numbers internally in the computer is fixed. As you probably know a float uses 32 bits and a double 64. This means that when arithmetical operations are performed, the result may not be exact. So operations on numbers in fixed-size representation also tend to introduce small errors.

The result is what you see in your example. The combination of conversion errors and fixed-size arithmetic errors show up as a "ripple" in the result.

These kinds of errors are fundamental to digital computers so they will always be present. One way to handle them is to round the result of a calculation. As you can see the error is far smaller than the 2 digits of precision you've used in the input numbers. If you round the output to the same precision the error disappears and the result is "correct".

Also note that programmers must watch out so formulas they use don't magnify those small fundamental and unavoidable errors. Such formulas are called ill-conditioned and there's a whole branch of math called numerical mathematics which is dealing with that.

Ulf Dittmer

Rancher

Posts: 42966

73

posted 6 years ago

- 0

Please UseAMeaningfulSubjectLine. You can edit the subject using the button.

As to your question, see #20 in the http://faq.javaranch.com/java/JavaBeginnersFaq.

As to your question, see #20 in the http://faq.javaranch.com/java/JavaBeginnersFaq.

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