Nombor bukan nisbah adalah salah satu yang anda tidak boleh menulis ke bawah sebagai sebahagian kecil kerana perpuluhan itu akan diteruskan, tanpa berakhir, tanpa yang diulang-ulang. Contoh-contoh nombor bukan nisbah akan Pi, nombor ‘e’ atau Euler dan nisbah keemasan. Anda boleh mencari maklumat lanut di sini! http://www.internetdict.com/ms/answers/what-is-irrational-number.html 26/8 internetdict
Nombor nisbah ialah nombor yang yang boleh diungkapkan sebagai nisbah dua integer . Nombor nisbah yang bukan integer biasanya ditulis dalam bentuk pecahan pecahan.. Contohcontoh nombor nisbah ialah ", , dan ".#. $ dan e adalah antara contoh-contoh nombor bukan nisbahkerana nisbah kerana tidak boleh diungkapkan sebagai nisbah dua ingeter. %et bagi semua nombor nisbah ditakri&kan sebagai,
di mana
ialah set bagi semua integer.
https!''ms.wikipedia.org'wiki'No https!''ms.wikiped ia.org'wiki'Nombor(nisba mbor(nisbahh )*'+ wikipedia An
Irrational Number is
a real number that
cannot be
written as a
simple fraction. Irrational means
not Rational
Examples:
https!''www.mathsis&un.co https!''www. mathsis&un.com'irrational m'irrational-numbers.html -numbers.html )*'+ math is &un An irrational number is a number that cannot be epressed as a &raction &or any integers rrational numbers hae decimal epansions that neither terminate nor become periodic. Eery transcendental number is number is irrational.
and .
/here is no standard notation &or the set o& irrational numbers, but the notations , , or , where the bar, minus sign, or backslash indicates the set complement o& the rational numbers oer the reals , could all be used. /he most &amous irrational number is
, sometimes called Pythagoras0s constant. 1egend has it that
the Pythagorean philosopher 2ippasus used geometric methods to demonstrate the irrationality o& while at sea and, upon noti&ying his comrades o& his great discoery, was immediately thrown oerboard by the &anatic Pythagoreans. 3ther eamples include
, , , etc. /he Erd4s-5orwein constant 6"7
6)7
687 63E% A9*#::); Erd4s "<:+, =uy "<<:7, where is the numbers o& diisors o& , and a set o& generali>ations 65orwein "<<)7 are also known to be irrational 65ailey and Crandall )99)7. Numbers o& the &orm are irrational unless is the th power o& an integer . Numbers o& the &orm , where is the logarithm, are irrational i& and are integers, one o& which has a prime &actor which the other lacks. is irrational &or rational . is irrational &or eery rational number 6Nien "<#*, %teens "<<<7, and 6&or measured in degrees7 is irrational &or eery rational with the eception o& 6Nien "<#*7. is irrational &or eery rational 6%teens "<<<7. /he irrationality o& e was proen by Euler in "?8?; &or the general case, see 2ardy and @right 6"eta &unction7 was proed irrational by Apry 6"
and
7, and . Nesterenko 6"<<*7 proed that is irrational. are algebraically independent, but it was not preiously known
=ien a polynomial euation
(4 ) where are
are integers, the roots , , and .
are either integral or irrational. &
rrationality has not yet been established &or constant7.
,
,
, or
6where
is irrational, then so
is the Euler-ascheroni
Fuadratic surds are irrational numbers which hae periodic continued &ractions. 2urwit>0s irrational number theorem gies bounds o& the &orm
(5 ) &or the best rational approimation possible &or an arbitrary irrational number , where the are called 1agrange numbers and get steadily larger &or each GbadG set o& irrational numbers which is ecluded. /he series
(6 ) where
is the diisor &unction, is irrational &or
and ).
http!''mathworld.wol&ram.com'rrationalNumber.html )*'+ wol&ram mathworld Irrational numbers are non-terminating and non-recurring. Example:
is the irrational i.e.,
H ".:":)"8#*)8?89#:?
2. We can obtain infinite number of irrationals between two irrational numbers. Example: @rite two possible irrational numbers between ) and 8.
Consider the suares o& ) and 8 )) H : and D H GMem2e 6"7
# and * lie between
and
lie between ) and 8. /he reuired possible irrational numbers are 5√ and 6√ 3. we can represents an irrational numbers on the number line Example: 2 √ an irrational number, on the number line.
4. best-known irrational numbers are 6the ratio o& the circum&erence o& a per&ect circle to its diameter7 ! e "the base o& natural logarithms7 #. Irrational numbers are also infinite. i.e.! irrational numbers are uncountable Example: All numbers without per&ect suare...like $. %he product of two irrational numbers ma& be rational or irrational. Example:'(
is irrational,
) is a rational number. 2(
, so, here two irrational numbers multiply to gie an irrational number. ). *n irrational number di+ided b& an irrational number e,uals rational or irrational number. Example:
" is the rational number. is a irrational number . um of the two irrational numbers is irrational Example:
is the irrational number. /. subtraction of the irrational number ma& be rational or irrational. Example: '(
is a rational number
2(
is a irrational number http://math.tutor!ista.com/number-s"stem/irrational-numbers.html 2#/8 tutor!ista.com
Where can &ou find special irrational numbers /he answer to this depends on what you consider Gspecial.G athematicians hae proed that certain special numbers are irrational, &or eample Pi and e. /he number e is the base o& natural logarithms. t is irrational, ust like Pi, and has the approimate alue ).?"+)+"+)+:#<9:#)8#89*.... t0s not easy to ust Gcome upG with such special numbers. 5ut you can easily &ind more irrational numbers using most suare roots. Dor eample, what do you think o& I) J "K s the result o& that addition a rational or an irrational numberK 2ow can you knowK @hat about other sums where you add one irrational number and one rational number, &or eample I# J "':K Lou can also add two irrational numbers, and the sum will be many times irrational. Not always though; &or eample, e J 6Me7 H 9, and 9 is rational een though both e and Me are irrational. 3r, take " J I8 and " M I8 and add these two irrational numbers what do you getK & you multiply or diide an irrational number by a rational number, you get an irrational number. Dor eample, I?'"9999 is an irrational number. Let another possibility to &ind irrational numbers is to multiply suare roots and other irrational numbers. %ometimes that results in a rational number though
6whenK7. athematicians hae also studied what happens i& you raise an irrational number to a rational or irrational power. Let more irrational numbers arise when you take logarithms or calculate sines, cosines, and tangents. /hey don0t hae any special names, but are ust called Gsine o& ?9 degreesG or Gbase "9 logarithm o& #G, etc . Lour calculator will gie you decimal approimations to these. http://www.homeschoolmath.net/teachin$/irrational%numbers.php 28/8 home school math.net
The Taj Mahal in India was also constructed using the Golden Ratio. The main building of the Taj Mahal was designed using the Golden Ratio. This is why it looks so perfect. The rectangles that served as the basic outline for the exterior of the building were all in the Golden Proportion.
http://thewondero&phib"'e!inandashle".weebl".com/the-$olden-ratio-inarchitecture.html 28/8 the wonder o& phi
Persamaan ini mempunyai satu penyelesaian positi& dalam nombor tak nisbah algebra!
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