Fractions2 - Welcome

Fractions2 - Welcome

for iPad

Welcome to the Fractions Calculator2 help documentation.

April 2010.

iPad version

March 2010

v1.1.3 ‘=’ makes a mixed fraction

Sept 2009

V1.1.2 is -3^2=-9 or 9, you choose.

This version offers the ability to email the calculator tape to someone, if email is supported on the device. It also allows you choose between pure math mode and excel mode where the order of precedence for negation and power is different.

Aug 19th,

v1.0.8 provides faster factorial calculations on the iPhone 3G S.

Fractions unlimited is a calculator that does Fractions, although there are a number of calculators on the App store that do fractions, this application is unique in the way it handles unlimited sized fractions, and factorials as it attempts to preserve numerical accuracy.

We also support brackets, floating point entry, and x raised to y, plus have a “paper tape”. Other calculators on the store lack those features.

For example you can enter

512!/513! which is 1/513, this requires manipulation of a 1,170 and 1,167 digit number. The actual calculation is found below the help text.

“½” Mixed Fraction or Fraction key

To Enter 42 3/8 we tap the “½” also described as the “/” key

'4' '2' '½' '½' '3' '½' '8'

that gives

42_3/8

Note the tapping of the '½' key twice to indicate you are entering a mixed fraction. Also if you just enter 42_7 that will evaluate to 42+7/1 or 49 because the 7/1 is implied.

Order of Precedence

! Factorial

½ Fraction operator

_ Mixed Fraction operator

^ raise to the power of

- negated

multiply, divide

plus and minus

So 1_1/2^2 is 9/4 because we calculate it as (1+1/2)^2

-3^2 is -9 because it is -(3^2)

-5_3/4^2 is -33_1/16 because it is -((5+3/4)^2)

Huh? isn’t -3^2 = 9?

{ Our Version 1.1.2 will allow you choose between pure math mode and excel mode where the order of precedence for negation and power is different, however read on for the arguments about which is correct}

Check WolfRam Research's Alpha web site:

http://www.wolframalpha.com/input/?i=-3%5E2

It say '-9'

That is our IMPARTIAL reviewer and how we cross checked all our calculations for proper order of operation in our test phase, in fact we have 100's of test cases to confirm our math is correct.

Don't trust WolfRam Research? Can you trust WikipediA?

Then http://en.wikipedia.org/wiki/Order_of_operations

See Examples: Specific cases (5).

Oddly they say -9 too!

But?

We allow for two different orders, a pure math order, and a second order that follows Microsoft Excel concepts.

The pure math order is:

! Factorial

½ Fraction operator

_ Mixed Fraction operator

^ raise to the power of

- negated

multiply, divide

plus and minus

So 1_1/2^2 is 9/4 because we calculate it as (1+1/2)^2

-3^2 is -9 because it is -(3^2)

-5_3/4^2 is -33_1/16 because it is -((5+3/4)^2)

The Microsoft Excel order is:

! Factorial

½ Fraction operator

_ Mixed Fraction operator

- negated

^ raise to the power of

multiply, divide

plus and minus

-3^2 is 9 because it is (-3)^2, and -3^3 is -27.

-5_3/4^2 is 33_1/16 because it is (-(5+3/4)^2)

This order follows the pattern of most calculators. It is set by turning on the -3^2=9 switch in the Settings Application for Fractions, for historical reasons the pure math order is the default.

Fractions versus Divide

“/” is not “÷”

“½” means number/number to make a fraction

“÷” means expression divide by expression.

saying

1 / 3 ÷ 4 / 3 = 1/4

is very different than

1/3 / 4/3 = 1/36

We note because of ambiguity in calculating the above we would calculate it as ((1/3)/4)/3. Therefore you should use the brackets keys if you intend to calculate the value as (1/3) / (4/3). Or obviously it could be better expressed as 1/3 ÷ 4/3 and then no brackets are needed.

! Factorial

The “!” key as you saw indicates factorial. But how big? Well try 5000!, that might take a few seconds and the number is 16,326 digits long. Once a calculation takes more than 2 seconds we put up the swirling wait icon.

Oh and 5000!/4999!= is 5000

The time consuming part of the calculation is expressing large numbers as written decimals in the text area, so asking for 5000! takes a long time, but asking for 5000!/4000!= happens in a few seconds.

^ Raise to the Power of:

The “^” key let’s you perform x^y say for example

2^151 ->

2854495385411919762116571938898990272765493248

Your regular calculator may have problems showing that

Do not forget -3^2 in math terms is -9 not 9, but in Excel mode it is 9. Which mode you pick is a personal decision, but we do note the Apple's calculator mimics Excel.

“Fraction<->Float” mixed fraction/float

Shows the mixed fraction value of the last calculated result, pressing again shows the floating point value.

45÷23=

45/23

F<>F gives

1_22/23

pressing F<>F again gives

1.956521739130435

Obviously the floating point value is an approximation of the fraction as a double precision number, and really large numbers will calculate to float Infinity or -Infinity.

Floating Numbers

Fractions allows you to enter Floating point numbers, these numbers are then converted to approximated fractions. Floating point numbers are double precision based, and they are immediately converted to fractions when entered.

“e” and the “-” keys

The “e” and the “-” keys help you enter the - and e for negative number or negative exponents:

0.3003 -> (3003/10000)

-0.333e-5 -> (-333/100000000)

-0.333e5 -> -33300

or for example

5--3 -> 8 which is 5 minus negative 3

STO

Stores the calculated value or current number into a memory cell.

RCL

Pulls the remembered value into the current calculation, it replaces the current number.

Calculator tape.

As you compute numbers we remember the calculations and store the tape between sessions.

1+2=

3

1/4÷4.332+45/69=

35365/49818

We limit the tape to 8,096 characters and save the tape between sessions, along with the state of the calculator including the memory entry. If the tape is greater than 8096 characters it is truncated to a smaller size on a calculation boundary.

C

You can use the C key to delete the last digit/operator entered. Tap and hold for a second to get a prompt, otherwise quick taps will delete one character backwards.

You can also swipe the calculator tape, left or right to get a dialog asking what you want to delete.

The Mail Button.

The Mail button allows you to email the "Paper Tape" to someone, or yourself. We write the version number of the Calculator on the tape along with the date and time, and the setting for the order of precedence. When you conclude the email session we write the status of the email processing to the paper tape.

Email must be activated on your device for the Mail button to be enabled.

Example email:

Fractions Calculator Unlimited Tape Version 1.1.0

2009-08-25 10:53:56 -0700

Setting -3^2=9 is OFF, so -3^2=-9

5_7/8*3_2/3=

517/24

21_13/24

21.54166666666667

Sent from my iPhone

The Info Button.

Tapping the info button lets you see the help text, and a hyper link to our Web Site.

Sound

The device's Settings application lets you set the Sound On/Off for Fractions, use the Fractions sub-panel.

512!/513! the actual values are:

34772897931326053632830459175456047119922

50655643514570342474831551610412066352543

47320985033950225364432243311021394545295

00170207006901326415311326093794135871186

40447161868610408995574973614275882823562

54968425012480396855239725120562512065555

82212170878644362079924655095918723202683

80814151785881725352800207863134700768597

39980965720873849904291373826841584712798

61843038733804232977180172476769109501954

57589869427325150335515295950098769992795

53931070378592917099002397061907147143424

11325211758595081785089661843399414023282

33164321874103563412623863324969543199731

30407342567282027398579382543048456876800

86234992814041190543127619743567460328184

25307441775273658857216295122538723866131

18821540847897493107398381956081763695236

42279588029620430177080880947714763242863

92990388330462645858348881588473877378418

43413664892833586209196366979775748895821

82692404005784514028752223867508213757031

59545267274370949049147967826410007407778

97919134093393530422760955140211387173650

04735834735337923438760926130667377328141

28930269419274240000000000000000000000000

00000000000000000000000000000000000000000

00000000000000000000000000000000000000000

0000000000000000000

/

17838496638770265513642025557008952172520

24586345122974585689588585976141390038854

80175665322416465611953740818553975401736

33587316194540380451054710286116391701918

62549394038597139814729961464123527888487

58798802031402443586737978986848568689630

13674843660744557747001348064206305002976

79357659866157325105986506633788101494290

46610235414808285000901474773169732957665

69125478870441571517293428480582553174502

69743603016217802122119346822400669006304

11166639104218166471788229692758366484576

57009833632159276955750996525663899393943

83613297121415128030676041885709375661462

15898966737015680055471223244583858377798

84238551313603130748624468928450107148358

52182717630715386993751959397862365343325

29955450454971413964095369943469944775656

28489428659195280680842491926177673543589

19604069213527337325332976254887099095128

65671210090023629725317736260624959183556

59721203254967455696749890844031713657357

20846722111752296862212907494948333800190

61632515789910881106876369986928441620082

47429483219228354724084355105032364569336

48141228212087685120000000000000000000000

00000000000000000000000000000000000000000

00000000000000000000000000000000000000000

0000000000000000000000

As you can see Fractions deals with really large numbers.

Contact Us Jun 3th, 2009 v 1.0.7

Aug 19th, 2009 v1.0.8

Sept 17th, 2009 v1.1.2