In secondary school we should be able to recognise whole numbers and know that there are other types of number as well. At this level we need to explore the different types of number a bit further and maybe introduce others.
This topic can also be discussed in terms of 'place value' as Maths teachers see the importance is understanding 'place value' rather than just knowing about the decimal point and money which is often given to two decimal places.
Decimal numbers is very closely tied into 'units' of measurement and their significance can be learned by considering changing units. Consider changing the length of something from metres to centimetres or millimetres.
Decimal numbers also tie in closely with fractions and percentages. Converting a value between decimals, fractions and percentages is an important skill. This should also reinforce to the student that these are just different ways of showing the same quantity.
Just another way to show a value. Because it is a value, we can add, subtract, multiply and divide but the techniques we use to do this need to be learned and mastered. Being able to work quickly with fractions helps us in algebra and further mathematics.
One important note with fractions: we often say "half of something" for example, "half of 6 is 3"; what we mean is "half times 6 is 3" and we can always replace "of" with "times" and vice-versa "times" with "of". So the next time you asked to multiply two fractions together just think "of" (half times a quarter is half OF a quarter).
Percentages are decimals multiplied by 100%. Note that % is so important that the symbol is on the keyboard. So: 0.25 is the same as 0.25 x 100% = 25%.
When teachers speak about 'rational numbers' all they mean is that they are numbers that can be represented as a fraction where there is a whole number on top and a whole number on the bottom. Quick question 1: What is the top and bottom of a fraction called?
So IRRATIONAL NUMBERS cannot be represented by a fraction with numerator and denominator both whole numbers.
Quick question 2: what do we get if the numerator or denominator is zero?
Quick question 3: how many answers are there to quick question 2? and why?
When we want to work with very large or very small values we use an invented representation of these quantities. This representation is called SCIENTIFIC NOTATION (we find very big things and very small things in Science subjects). To get to using this notation we need to understand decimals AND we need what is meant by powers. Being able to multiply and divide in powers of ten is also very important.
Myth: to multiply by ten we add a zero. WHY: because if we add a zero at the end of a decimal nothing changes
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