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Significant Figures and Scientific Notation

For many students, the concepts of significant figures and scientific notation are initially daunting and confusing. It is not unusual for a student to confuse the idea of rounding to a certain number of decimal places as being the same as rounding to a certain number of significant figures. Adding the concept of scientific notation into the mix can lead to the student being so uncertain as to how to write their answer for a given question.

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Infallible Calculator?

You may have seen the claim on the Internet that millions of people get the answer to the equation  6 \div 2\left(1 + 2\right)  (or similar) wrong. You may have even read the explanations by some people about why the answer should be 9 or should be 1. Let me clear it up and explain why the answer is most definitely 1, but why the calculator (and others) give 9.

Firstly, the important thing to recognise is that this equation, like all others, is subject to the Order of Operations, which states that we must solve the contents of the brackets first. Thus our equation becomes  6 \div 2(3) .

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The Secret to Success in Mathematics

TInSpire CAS Calculator with warning sign

There are so many people who struggle with mathematics and yet some people seem to have no trouble whatsoever. Is there something different in their DNA or some super advanced part of their brains, or do they simply know some secret trick that helps them in their understanding?

The answer is a little of the second, but mostly the last. Scientific research suggests that those who are good at mathematics do have some areas of their brain more active during mathematical activities, however, this increased brain activity could be a result of increased mathematical training. Much like how an athlete’s muscles improve with training, regular mathematical exercises help to improve the performance of those brain areas associated with mathematics. Again, like an athlete in training, there needs to be some underlying skills and a good coach. All of us possess the minimum underlying skills, but not all of us are fortunate enough to have a good coach at the critical time when we are ready to start serious mathematical training.

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