It's not a bug. It is just that calculators and computers can only do arithmetic imperfectly. Numbers are represented at machine code level by binary numbers. All fractions that do not have a power of two as the denominator have a recurring binary form. Since no machine can hold an infinite number of binary digits, it is inevitable that the representation will involve some sort of truncation of the true value. This leads to tiny errors between the value calculated and the true answer.

In the early days of calculators it was much more common to find such errors arising. Two things (at least two; there must be more that I don't know about) can improve the situation. (i) Increase the number of binary digits used to represent the number; (ii) use guard digits. The latter means that more digits are used than are displayed. The guard digits are used to round off the displayed results. This eliminates a lot of the problem.

On a calculator you can reveal the guard digits by doing a sum and then subtracting the displayed answer from itself. The difference is the guard. If rounding up has occurred you need to adjust what you see displayed by one to allow for the rounding.

Bob

]]>It is a property of how computers and mathematics mix. Once you know about it you are prepared. We will go over it when the the time comes.

]]>One way or another all math programs will do this, even Mathematica.

Thats Funny.

]]>1. Open calculator.

2. Enter a square number like 25.

3. Click on the square root button in the calculator.

4. Now subtract the result from the square root of the number, in this case 5.

5. Click '=' button on the calculator and note that the result is not 0.

they have a bug

]]>Yes, we could come up with something better. A human brain! But I think that has already been made.

Here is a whole bunch of examples that I worked on for MIF:

]]>5) You never use the quadratic formula to solve a quadratic equation because on a computer it will give inaccurate results.

Would you give an example?

]]>Isn't this the precision stuff you always mention, bobbym?

Computer math ≠ human math

Okay, first you must get the spiel.

The hardest thing for computers to do is arithmetic. People find that amazing but it is true. The problem is not a bug but it is inherent in the way computers do arithmetic.

1) To a computer the number line is not solid like they draw it in mathematics. Instead it looks like the dots and dashes of morse code. This is because some numbers do not exist for a computer. For instance there is no 1 / 3 on its number line, just a big hole.

2) (a - b)(a+b)≠(a^2 - b^2). Algebraically equal expressions are not equal to a computer.

3) Addition is not commutative.

The order of addition can drastically affect the answer!

4) A computer can not subtract or multiply without possible disastrous error.

5) You never use the quadratic formula to solve a quadratic equation because on a computer it will give inaccurate results.

6) Newton's iteration though taught is rarely the best one for the job.

7) A computer can not compare theoretically equal quantities.

and many more.

]]>I didn't understand what you're talking of

]]>