Why do some calculators give different answers?

Answer 1

The difference in the working memory and significant digits, as well as the ability to handle mathematical operations in their proper order, can all cause one calculator to give a different answer than another.

There are two main types of calculator: scientific and non-scientific.

The non-scientific calculators are often simple calculators with few operations beyond arithmetic and memory operations (although they may have square roots). They are generally intended as a desktop calculator for use by people who have to add up lots of numbers. As such, they are very simple, and every operation (+-×÷) works on the last number displayed. This last displayed number could be the result of the last calculation. Thus, if you enter 1 + 2 × 3, when the multiply key is pressed, the calculation of 1 + 2 is done and the result of that is multiplied by the next number entered, that is, the result of 1 + 2 × 3 is 9 (since 1 + 2 = 3, and 3 × 3 = 9). These calculators do not have keys for parentheses, nor can they do exponential display. They are limited to something like ±0.0000001 to ±99,999,999, up to eight digits of display. Tthe more digits before the decimal point, the less that can be after it.

In contrast, scientific calculators have many more functions (e,g. trigonometric, powers, logs) and know about proper mathematical order of operations. Thus with one of these types of calculators entering 1 + 2 × 3 will give the result of 7, since the multiply is done first and then the result of that is added to the 1 - it has calculated 1 + (2 × 3). They DO have keys for parentheses, as the proper order of doing operations may need to be overridden, eg (1 + 2) × 3 to get the same result as a simple, non-scientific calculator. Scientific calculators can also handle exponential numbers, so they can handle a much larger range of numbers (something like ±1 × 10^-99 to 9.9999999 × 10^99).

There is a slight variation in the range that different scientific calculators can handle. This range depends on how much internal storage is allocated to store each floating point number. Most scientific calculators these days will display nine digits with a further two for the exponent, though some may only allow seven or eight digits, and some may allow ten or 11 digits, or possibly three digits for the exponent. Internally, they will usually work to one or two digits more than the displayed digits so that the result displayed is rounded properly.

In summary, the difference in the working memory and significant digits, as well as the ability to handle mathematical operations in their proper order, can all cause one calculator to give a different answer than another.

Answer 2

Different calculators may work with different precision. However, the main discrepancy is that scientific calculators usually do multiplications and divisions before they do additions and subtractions (as they should); whereas most simple calculators don't (for simplicity of design, and perhaps so as not to confuse users who are unaware of the standard rules). As a result, for example, the expression:1 + 2 x 3

will be incorrectly shown as 9 by simple calculators, whereas a scientific calculator will correctly do the multiplication first.

Answer 3

The answer to the question depends on what it is you are trying to calculate. Assuming that there are no errors in entering the numbers and operators - including implied brackets - then there are two possible reasons. One possible reason is rounding. If a sequence of calculations is to be carried out, it will make a difference whether the previous results are used at the next stage or whether they are re-entered in a rounded form. Another reason for different answers - which applies only to trigonometry - is whether angles are measured in degrees or radians: check the set-up.

Answer 4

It is not different answers but different approximations and different truncation errors. Some calculators have more accuracies than others. This is the reason.