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Unformatted text preview: Maths Study Sheet ?' decimals dealing with number systems part 4 This WIT cunsists {if 4 parts Part 4: Yeu are intreduced te seme sets uf numbers. When veu have werked threugh the Part, veu will have met
I ratienal numbers I irratienal numbers
Ir real numbers and their representatiens en a real number ]jne. Prerequisites:
Seme familiarity with integers, fractiens and decimals. All the numbers we have enceuntered se Far, natural (cuunting) numbers,
integers (pesitive and negative whele numbers tngether with stern} and
fractiensf decimals which terminate er recur in a pattern, are knuwn as ratiunal numbers. It is, nf cuurse, pessible re write a decimal number which gees en fer ever and
which dries nut recur in a pattern. F'crr instance, 0.1269375]? . . . . There are same special numbers which eccur in mathematics er science which
are at this kind. They are dennted by a special letter because ef their usefulness. Examples are 31' and ‘5’.
It is pessible te give enlv appresimate values fer these numbers. We eitcn use ﬂI'm£31.14 and F 3.2718 giving 2 and 3 decimal pace accuracy
respectively. Numbers el this kind are called irratienal numbers. The ratiunals and irratienals tegcthcr make up the set ct real numbers. The}: can each be represented by a peint en a line, knewn as the
real number line. —0 35 0.25 1.6 e 11: Integers Irratienal
“1.1th11: = [gal
numb ers Ceunting
numbers
1,2,3, . . . Ratienal numbers Every real number has a pesitien en this line, and every peint en the line
eerrespends te a real number. i‘er man},I ef us this is all we’ll ever need te knew abeut numbers. llewever, in erder te selve seine preblems vvhieh eeeurs in srienee and engi
neering, this system ean be extended even further. r1 very,I simple inventien, giving a name [i er 3] te the number “is” ‘1 leads te a
set ef temples: numbers, whieh ineludes all the real numbers. Hewever, that is a challenge fer the future! ...
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 Spring '11
 DR.MCDONALD

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