4 Doing longer calculations using your calculator
The volume of wood (in cubic metres) contained in a log of length metres with a distance around its middle of metres is given by the formula
For a log of length 1.5 m with a distance around the middle of 92 cm, this becomes
In this section we consider several different approaches that can be used to evaluate this and other more complex expressions using different functions on your calculator. While the first method – considered in Activity 9 – is probably the most straightforward for this relatively simple expression, it is useful to see how you might use other calculator functions when you are faced with more complicated expressions to evaluate.
The expression for the volume of wood requires the value of . You could enter an approximate value for by hand, but this is time-consuming and may be prone to error. The calculator has an approximation for built into it, which is obtained using the key sequence .
The key is located on the bottom row of the keypad.
Activity 9 Using the fraction key
The most obvious way of calculating is to enter it as a fraction on your calculator.
What key sequence is needed, and what is the final answer to 3 significant figures?
(to 3 significant figures).
The key sequence used was .
Note that it is not strictly necessary to include the multiplication between the 4 and the in the denominator since if the sign is omitted, it will be assumed by the calculator.
Another way to carry out the calculation in Activity 9 is to use the key.
Activity 10 Using the key
You will not obtain the correct answer to the calculation
if you type
into your calculator and press . Can you explain why? Insert a pair of brackets into the expression with the ÷ sign so that it will give the correct answer. Then type this new expression into the calculator and check that you obtain the same answer as in the activity above.
Typing into the calculator and pressing will not give the correct answer because the calculator will follow the BIDMAS rules and divide by 4 and then multiply by , instead of dividing by .
To obtain the correct result, you have to type . (Alternatively, you can type .)
(Note that on some later models of the calculator, the correct answer is obtained without adding the brackets to the denominator; however it is good practice to add the brackets to ensure the correct calculation is carried out).