Calculators have become as ubiquitous as pencils, and you have to be at least as old as I am to remember a time when they were an expensive luxury that you weren’t allowed to use in school – like mobile phones were only a few years ago! However, also like phones, most people don’t really know half the things their calculator does – and even when you think you do, they can still catch you out, as I discovered yesterday in a lesson. (Toby, if you’re out there this one’s for you!)
So here are a few things you might want to remember. They refer to the standard Casio fx-83 machines that are commonest in schools these days. (Mine is an fx-83GT PLUS).
1. The manual
Don’t throw it away with the packaging! It’s not the easiest thing to read, but it is useful, especially when your best friend has switched your calculator into a mode you don’t understand and can’t get it back.
If you have thrown it away, or the dog ate it as a side dish to your homework, all is not lost. You can download Casio manuals from here:
Most of the time, you will want mode 1 (COMP) for ordinary computation. Press the MODE button, then choose option 1.
The TABLE mode (mode 3) is useful if you have to work out lots of values to plot a graph of an equation. f(x) = means the same as y = for this. Enter the equation using the ALPHA button followed by the right bracket button to get an x when you need one. Then specify the start and end values you want, and the step value (that’s the gap between your x values), press enter and you will have a table of x and y values all ready to plot. And remember to put the calculator back into COMP mode when you’re done.
Enter the setup menu by pressing SHIFT then MODE. Options 1 and 2 let you choose how the calculator displays fractions, surds and so on. You will probably prefer option 1 (MthIO), followed by output option 1 (MathO). These let you enter fractions the way they look on paper, and display results as fractions, surds and multiples of Pi whenever possible. To get the decimal equivalent, press the S↔D button.
You shouldn’t need the other setup options for GCSE, unless somebody (perhaps a friend in the sixth form) has changed the way your calculator handles angles. You want option 3 for degrees. A letter D appears at the top of the display when this has been selected.
4. Recurring decimals
If you enter 1/7 then press = , the display will show 0.142857 with dots over the 1 and the 7 to show that these digits recur. (Pressing = again gives as many digits as the display will hold, with the last digit rounded. A third press gets you back to the fraction).
You can also enter a recurring decimal by hand, by pressing SHIFT followed by the x2 button when you want to enter the repeated digits. You get a box with the dot over it, and type the numbers you want into it. Typing 0 . SHIFT x2 142857 = will give an answer of 1/7. This is great for checking those ‘recurring decimal to fraction’ problems, but won’t get you any marks in the exam, as you have to show your working.
Very large recurring sequences may not show the right hand dot straight away. For example 1/17 displays 0.0588235294117 with a dot over the first decimal place and an arrow pointing right after the 7. Pressing the right arrow key three times displays an extra 647 with the right hand dot over the final digit.
You can express an integer as a product of prime factors by pressing SHIFT followed by the ‘degrees, minutes, seconds’ button underneath the square root button. For example, 47952 is expressed as 24 x 34 x 37. For some reason, the calculator only factorises answers, so you need to type in the number, press = and then factorise it.
(In passing, it mystifies me that every calculator I have owned in the last 20 years has the ‘degrees, minutes, seconds’ button, which I have never used (not once!) and yet requires me to press SHIFT every time I want the Pi button. Sharp make calculators with a top level Pi button, but for some reason Casio choose not to…)
6. Squaring negative numbers
Calculators do BIDMAS! That is, when you enter something they look at brackets first, then indices, then division, multiplication, addition and subtraction.
This means that when you enter -3 then press x2 = you get an answer of -9.
You did know that’s wrong, didn’t you? (A minus times a minus makes a plus?)
It only does this when you actually type in the negative number. (It ‘knows’ the sign of the answer to something like 4 – 7 and will square it correctly.) So to make sure you aren’t embarrassed by a negative square:
a) Type in the number, press =, then square it.
b) Put brackets round the number, then square.
c) Don’t put the minus sign in at all!! After all, you know the answer should be
positive. Save keystrokes, save energy.
7. Mixed fractions
The best way to enter these is to press the shift button followed by the fractions button (in MthIO mode), then type the numbers into the boxes.
e.g for 2 ½ press shift, fraction, 2, right arrow, 1, down arrow, 2
This gives you the correct decimal value of 2.5 when you press = and S↔D.
The way NOT to do it is to type the fraction, then backspace and enter the whole number to the left of it.
e.g fraction, 1, down arrow, 2
then either right arrow twice or left arrow 4 times to get the cursor on the left side,
then 2 for the whole number
If you now press =, the answer is 1.
The calculator has interpreted what you did as 2 x ½ !!
I have no idea why this happens, but we had a fun time in yesterday’s lesson figuring out exactly what was going on….
Don’t do it!