Numerical reasoning tests are starting to let you use a calculator, in part because everyone has a calculator to hand most of the time in work applications. In a numerical reasoning test this is not an undisguised blessing. Calculators, if you make a mistake, give you the wrong answer very confidently.
There are two parts to using a calculator you need to think about:
- Does your calculator work mathematically? If you put in 1+2X3 what answer do you get? You should get 7, not 9. This is because maths has an order of precedence of operations - you can remember this with the acronym BODMAS or similar.
- Things in Brackets are the most important (apply the rules again to the things inside the bracket if necessary.
- Then Powers Of: things like x2 or 173.
- Next, and the same level of precedence you get Divison and Multiplication.
- Finally, and at the same level as each other you get Addition and Subtraction.
- Is the answer you get reasonable?
We've looked at estimations already. Use that skill to check the answer your calculator gives you makes sense. A misplacing of the decimal point, hitting 9 rather than 6, or 4 rather than 1 can make quite a big difference in your answer, big enough that a decent estimate will make you think again.
Multiplication and division and addition and subtraction being paired like this make sense if you remember they're reverse functions for each other. In BODMAS terms 1 + 2 X 3 means do the multiplication first, 2 X 3 = 6, then 1 + 6 =7. Cheaper calculators often work out each answer in order, so 1+ 2 = 3. 3 X 3 =9. If you have a calculator that does this, you need, when faced with these problems to reorder the calculation to make sure the calculator gives the correct answer.
Significant figures and precision
Using a calculator brings up the issue of significant figures. If you try 1/3 on a calculator you will get 0.3333333 with enough 3's to fill the display. Where do you stop writing the 3's down? More importantly, if given the sum 32.157 ÷ 2.1 you will get the answer, depending on your calculator's display, 15.31285714285714285714. Should you write this all down? The answer is no: but where do you stop?
There are two approaches you can take here. 32.157 has 5 meaningful numbers, and 3 decimals places. 2.1 has 2 meaningful numbers (significant figures is the mathematical term, abbreviated to sig figs) and 1 decimal place. Normally you would limit yourself to lower limit of significant figures, in this case 2. With division it is common to add one to the lower number of sig figs, so you could stretch to 3 in this case. You may also consider keeping to the lower limit of decimals places. These would both suggest you stopped at 15.3.
There is some confusion that can arise about 0's. In 1701 there are 4 sig figs because the 0 in the middle is not simply showing place value. In the number 1700 there are only 2 sig figs because the last two 0's are only showing place value rather than precision.
The real confusion arises with decimal points and 0's. Is 17.00 two sig figs or four? Because of the decimal point it is four sig figs. The extra 0's in this case indicate precision, you could have just written 17, but the choice of 17.00 makes it clear that it is more precisely 17.
Final comments
Being able to use a calculator also moves you away into a situation where, although the maths won't be any harder, the numbers in the question will be harder. This can start from things like changing the numbers, rather than tickets costing $48, they'll cost $47.99, and build up to include having to give a precise answer rather than multiple choice questions.
Despite these drawbacks, using a calculator makes the basic number crunching easier, as long as you use it correctly. It is worth playing with a calculator for a while and seeing how you go with - just remember not to use it in the final exam for this course!
I am not in any way affiliated with Linden Lab. This site advertises my work within their virtual environment.
The terms Second Life, Linden Lab and SL are trademarks belonging to Linden Lab. No infringement of their trademark is intended. Usage here is nominative.