# Fractions or Decimals?

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

1. ### 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
2. ### 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

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Fractions are decimals and vice-versa. Yes?
We know that 0.5 = 5/10. You say?

nycmathguy, May 31, 2022
4. ### 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

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Can you explain repeating decimals versus non-repeating decimals?

nycmathguy, May 31, 2022
6. ### 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:

another example:

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

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nycmathguy, Jun 1, 2022
8. ### 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

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This is insanely cool.

nycmathguy, Jun 1, 2022
10. ### 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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