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Your Pocket Scientific Calculator
Error messages and other Nerd Stuff


This Page is only about different models of Casio fx-83 and fx-85 calculators.Much of this information can be found in the instructions that came with your calculator but in very small print and not (in my opinion) very easy to follow.

Error Messages

There are four main Error Messages. You can clear them either by using the AC key or by using the cursor control key to move to and correct the error.

Syntax Error means that you have made a mistake somewhere when you have entered a calculation, for example you have typed 5 + × 8 = (using two operators together).

Maths Error means you have tried to do something which is not permitted by the Rules of Maths, for example dividing by zero.

Stack Error means you have exceeded the capacity of the stack. Every time you enter a calculation it is stored. Most characters take up one byte of storage but some take up two or even three, and there is a limit of 99 bytes.If you enter several calculations the earlier ones are automatically deleted when the space is needed for new ones so you will only get this error if you are entering a very long calculation.

Parameter Error means your calculator has opened a bracket or a box for you to enter a number and you have entered something unexpected, for example a number containing a decimal point when your calculator was expecting an integer.

Errors

There are two circumstances when your calculator gives you an answer which would normally be regarded as wrong.

A Your calculator omits trailing zeros after the decimal point, so 3.75 + 4.25 gives the answer 8 rather than 8.00

B When we are rounding numbers the Rule is that if the number being rounded is exactly half way between the two possible answers we always round up, for example if we are rounding to two decimal places 6.425 rounds up to 6.43 rather than down to 6.42. When we are rounding negative numbers -4 is bigger than -5 so -4.5 should round up to -4 but your calculator rounds down to -5.

Two Cautions

There are two occasions when you must be absolutely certain that you understand how your calculator is working.

A Entering negative numbers.

The square of negative nine is not the same as negative nine squared: one is +81 and the other is -81 This is fully discussed on the Page on Entering negative numbers. The best advice is unless you are absolutely certain about what you are doing put negative numbers in brackets, for example (-9)²

B Implied multiplication

There are times, particularly when using brackets or algebra, when it is permitted, in fact expected, for you to omit the multiplication sign, for example 2ab means 2 × a × b. The multiplication sign is implied. According to the strict Rules of Maths multiplication and division are of equal rank, so if they are both present in a calculation they are done in the order in which they are written, for example

ImpMult1.gif - 1121 bytes

According to the strict Rules of Maths implied multiplication is of the same rank as ordinary multiplication so

ImpMult2.gif - 982 bytes

However some calculators take implied multiplication to be of higher rank than ordinary multiplication, so the multiplication is done before the division and therefore 3 ÷ 2π = 0.48. This is the result that most non-mathematicians would assume to be correct unless they had been told otherwise, and it is the way many calculators, including some Casio calculators, work. But many other calculators, including some other Casio calculators, work according to the strict Rules of Maths. Check how your calculator works now! The situation is therefore very confused; the safest way, which will always give you the correct answer on any calculator, is if an implied multiplication follows a division put it in brackets. This is discussed further on the Fractions Page.

A confusing fault

Several young people have e-mailed me about something which they have found confusing, and which I would regard as a design fault.

When you press the enter key the answer to the calculation appears in the lower part of the display. In maths mode the moment you press any key to start to enter another calculation the answer to the previous calculation is cleared, but in one line mode it is not, so until you press the enter key you have one calculation at the top of the display and the answer to a different calculation at the bottom.

Accuracy

If your calculator can store a number with 100% accuracy then it will, otherwise it will store it to about fifteen significant figures - this applies mainly to irrational numbers and very large and very small numbers. Similarly, if it can display a number exactly then it will, otherwise it will normally display it to ten significant figures. This means that there may be rounding errors in the tenth place. Rounding errors are cumulative so in problems involving repeated calculations, for example iterations, permutations and combinations, there may be more significant errors. However this will probably not matter too much in school exams and other school work.

Limitations

For reasons described on other Pages never ever regard a calculator app on a smartphone or tablet as a substitute for a proper scientific calculator.

Your calculator is necessarily much less powerful than a decent PC spreadsheet or other maths program. Here are some of its limitations, although you will be unlikely to come up against them unless you are using your calculator in situations where it might be more appropriate to use a PC.

It cannot handle numbers with an absolute value of less than 10-100 or more that 10100. There are slightly different limitations for some trigonometric and hyperbolic and other functions - these are described in the instruction book with your calculator.

It cannot find the prime factors of a composite number where two or more of the factors are themselves four or more digit primes.

It cannot work with recurring decimals where the recurring sequence is more than 58 digits long, for example 7 ÷ 59 is shown as a recurring decimal but 5 ÷ 97 is not. (Numbers between 59 and 97 do terminate or recur but with less than 58 digits in the sequence. If you are thinking what sort of nutter actually counts all 58 digits in a recurring number keep your thoughts to yourself please.) Recurring numbers are discussed on the Recurring Numbers Page.

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© Barry Gray August 2014