Fractions or Decimals?

Discussion in 'Basic Math' started by nycmathguy, May 31, 2022.

  1. nycmathguy

    nycmathguy

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    Which is easier to teach: fractions or decimals? Why? Which comes first in the math order of things to learn: fractions or decimals?
     
    nycmathguy, May 31, 2022
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  2. nycmathguy

    MathLover1

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    Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's difficulty with rational numbers in general.
    In my opinion, decimals are not generally easier to understand than fractions, though they are easier on some tasks.
     
    MathLover1, May 31, 2022
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  3. nycmathguy

    nycmathguy

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    Fractions are decimals and vice-versa. Yes?
    We know that 0.5 = 5/10. You say?
     
    nycmathguy, May 31, 2022
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  4. nycmathguy

    MathLover1

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    Some decimals can be written in fraction form. π is a transcendental number, but cannot be represented by an infinite continued fraction.
     
    MathLover1, May 31, 2022
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  5. nycmathguy

    nycmathguy

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    Can you explain repeating decimals versus non-repeating decimals?
     
    nycmathguy, May 31, 2022
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  6. nycmathguy

    MathLover1

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    A repeating decimal, also called recurring decimal, is a decimal number in which a digit or a set of digits repeats infinitely or without end. For example, the decimal number 6.333333333 is a repeating decimal. 6.333333333 has only 1 digit that repeats infinitely and that digit is 3.

    you can write as:
    upload_2022-5-31_17-51-10.jpeg

    another example:
    upload_2022-5-31_17-51-48.jpeg

    upload_2022-5-31_17-56-56.jpeg
    π is a transcendental number
    π =3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026........and so on

    which means it cannot be represented as a simple fraction, and those numbers cannot be represented as terminating or repeating decimals.
     
    MathLover1, May 31, 2022
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  7. nycmathguy

    nycmathguy

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    What about the number e?
     
    nycmathguy, Jun 1, 2022
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  8. nycmathguy

    MathLover1

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    just like π, e is a transcendental number

    e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931277361782154249992295763514822082698951936680331825288693984964651058209392398294887933203625094431173012381970684161403970198376793206832823764648042953118023287825098194558153017567173613320698112509961818815930416903515988885193458072738667385894228792284998920868058257492796104841984443634632449684875602336248270419786232090021609902353043699418491463140934317381436405462531520961836908887070167683964243781405927145635490613031072085103837505101157477041718986106873969655212671546889570350354021234078498193343210681701210056278802351930332247450158539047304199577770935036604169973297250886876966403555707162268447162560798826517871341951246652010305921236677194325278675398558944896970964097545918569563802363701621120477427228364896134225164450781824423529486363721417402388934412479635743702637552944483379980161254922785092577825620926226483262779333865664816277251640191059004916449982893150566047258027786318641551956532442586982946959308019152987211725563475463964479101459040905862984967912874068705048958586717479854667757573205681288459205413340539220001137863009455606881667400169842055804033637953764520304024322566135278369511778838638744396625322498506549958862342818997077332761717839280349465014345588970719425863987727547109629537415211151368350627526023264847287039207643100595841166120545297030236472549296669381151373227536450988890313602057248176585118063036442812314965507047510254465011727211555194866850800368532281831521960037356252794495158284188294787610852639813955990067376482922443752871846245780361929819713991475644882626039033814418232...
     
    MathLover1, Jun 1, 2022
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  9. nycmathguy

    nycmathguy

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    This is insanely cool.
     
    nycmathguy, Jun 1, 2022
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  10. nycmathguy

    Doz

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    it's different in different schools but in mind we learn fractions first
     
    Doz, Jun 14, 2022
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  11. nycmathguy

    nycmathguy

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    What do you mean by IN MIND?
     
    nycmathguy, Jun 17, 2022
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