Non-Beleivers

Apparently I have some non-believers in the class.  No problem.  Today we will take a field trip to solve the problem.

A few people are not sure that they believe what I told you about the fraction 1/998001.  They don’t believe a fraction can count from 0 to 970 without an error, and they don’t have a tool (a calculator or computer program) to check it out for themselves.

I can’t get angry about that.  I did not believe it either the first time I saw it.  I saw it on another website, and I was sure it had to be wrong.  So I decided to check it out for myself.

OK now, pay attention!  I want you to open another screen in your browser and go to: www.wolframalpha.com.  On the main screen you will see a place to type in a mathematical expression or a question.  Please type in “1/998001”, and then hit enter.

The screen that comes up will show the expression you typed in.  Below that you will see a box labeled input, then exact value, and then decimal approximation.  The decimal approximation shows a number that starts with a 1, but it is written in scientific notation (10 raised to the -6 power means you have to put 6 zeros in front of the 1.).  It also only counts up to 19.  No problem.  Do you see the button to the right that says “more digits” – click it – click it again – and keep clicking it until it won’t give you any more digits.

Now go down to the bottom of that box – if you move your cursor around at the bottom left of the box a small menu will pop up in yellow– click on the “A” in that box.  Now you can use your cursor to highlight the number, copy it and past it in a document file.  This is what you get (after you add the 6 zeros to the front of the number):

0.
000001002003004005006007008009010011012013014015
016017018019020021022023024025026027028029030031
032033034035036037038039040041042043044045046047
048049050051052053054055056057058059060061062063
064065066067068069070071072073074075076077078079
080081082083084085086087088089090091092093094095
096097098099100101102103104105106107108109110111
112113114115116117118119120121122123124125126127
128129130131132133134135136137138139140141142143
144145146147148149150151152153154155156157158159
160161162163164165166167168169170171172173174175
176177178179180181182183184185186187188189190191
192193194195196197198199200201202203204205206207
208209210211212213214215216217218219220221222223
224225226227228229230231232233234235236237238239
240241242243244245246247248249250251252253254255
256257258259260261262263264265266267268269270271
272273274275276277278279280281282283284285286287
288289290291292293294295296297298299300301302303
304305306307308309310311312313314315316317318319
320321322323324325326327328329330331332333334335
336337338339340341342343344345346347348349350351
352353354355356357358359360361362363364365366367
368369370371372373374375376377378379380381382383
384385386387388389390391392393394395396397398399
400401402403404405406407408409410411412413414415
416417418419420421422423424425426427428429430431
432433434435436437438439440441442443444445446447
448449450451452453454455456457458459460461462463
464465466467468469470471472473474475476477478479
480481482483484485486487488489490491492493494495
496497498499500501502503504505506507508509510511
512513514515516517518519520521522523524525526527
528529530531532533534535536537538539540541542543
544545546547548549550551552553554555556557558559
560561562563564565566567568569570571572573574575
576577578579580581582583584585586587588589590591
592593594595596597598599600601602603604605606607
608609610611612613614615616617618619620621622623
624625626627628629630631632633634635636637638639
640641642643644645646647648649650651652653654655
656657658659660661662663664665666667668669670671
672673674675676677678679680681682683684685686687
688689690691692693694695696697698699700701702703
704705706707708709710711712713714715716717718719
720721722723724725726727728729730731732733734735
736737738739740741742743744745746747748749750751
752753754755756757758759760761762763764765766767
768769770771772773774775776777778779780781782783
784785786787788789790791792793794795796797798799
800801802803804805806807808809810811812813814815
816817818819820821822823824825826827828829830831
832833834835836837838839840841842843844845846847
848849850851852853854855856857858859860861862863
864865866867868869870871872873874875876877878879
880881882883884885886887888889890891892893894895
896897898899900901902903904905906907908909910911
912913914915916917918919920921922923924925926927
928929930931932933934935936937938939940941942943
944945946947948949950951952953954955956957958959
960961962963964965966967968969970971972973974975
976977978979980981982983984985986987988989990991
992993994995996997999 (then it starts repeating)

000001002003004005006007008009010011012013014015
016017018019020021022023024025026027028029030031
032033034035036037038039040041042043044045046047
048049050051052053054055056057058059060061062063
064065066067068069070071072073074075076077078079
080081082083084085086087088089090091092093094…

This is a little hard to read, so I took the liberty to highlight the 000 (or zero written as three digits) right after the decimal point, and the 997 near the end.  Remember – it skips 998, and then does a 999.  I also made sure that each line begins and ends with a “three digit chunk” that is one of the numbers it is counting.  This fraction has a period of 2997 digits – and that is the end of the period.  After that you will notice that the pattern starts all over again.

Remember – not everything on the internet is true and I could be trying to fake you off.  So make sure you go to the Wolfram Alpha website and try it yourself.  If nothing else you will know that the Wolfram Alpha website can be a useful mathematical tool for you.

See you again soon,

David