simple-squiggle

A restricted subset of Squiggle
Log | Files | Refs | README

fractions.md (2976B)

      1 # Fractions
      2 
      3 For calculations with fractions, math.js supports a `Fraction` data type. 
      4 Fraction support is powered by [fraction.js](https://github.com/infusion/Fraction.js).
      5 Unlike [numbers](numbers.md) and [BigNumbers](./bignumbers.md), fractions can 
      6 store numbers with infinitely repeating decimals, for example `1/3 = 0.3333333...`, 
      7 which can be represented as `0.(3)`, or `2/7` which can be represented as `0.(285714)`.
      8 
      9 
     10 ## Usage
     11 
     12 A Fraction can be created using the function `fraction`:
     13 
     14 ```js
     15 math.fraction('1/3')   // Fraction, 1/3
     16 math.fraction(2, 3)    // Fraction, 2/3
     17 math.fraction('0.(3)') // Fraction, 1/3
     18 ```
     19 
     20 And can be used in functions like `add` and `multiply` like:
     21 
     22 ```js
     23 math.add(math.fraction('1/3'), math.fraction('1/6'))      // Fraction, 1/2
     24 math.multiply(math.fraction('1/4'), math.fraction('1/2')) // Fraction, 1/8
     25 ```
     26 
     27 Note that not all functions support fractions. For example trigonometric 
     28 functions doesn't support fractions. When not supported, the functions
     29 will convert the input to numbers and return a number as result.
     30 
     31 Most functions will determine the type of output from the type of input:
     32 a number as input will return a number as output, a Fraction as input returns
     33 a Fraction as output. Functions which cannot determine the type of output
     34 from the input (for example `math.evaluate`) use the default number type `number`,
     35 which can be configured when instantiating math.js. To configure the use of
     36 fractions instead of [numbers](numbers.md) by default, configure math.js like:
     37 
     38 ```js
     39 // Configure the default type of number: 'number' (default), 'BigNumber', or 'Fraction'
     40 math.config({
     41   number: 'Fraction'
     42 })
     43 
     44 // use the expression parser
     45 math.evaluate('0.32 + 0.08') // Fraction, 2/5
     46 ```
     47 
     48 ## Support
     49 
     50 The following functions support fractions:
     51 
     52 - Arithmetic functions: `abs`, `add`, `ceil`, `cube`, `divide`, `dotDivide`, `dotMultiply`, `fix`, `floor`, `gcd`, `mod`, `multiply`, `round`, `sign`, `square`, `subtract`, `unaryMinus`, `unaryPlus`.
     53 - Construction functions: `fraction`.
     54 - Relational functions: `compare`, `deepEqual`, `equal`, `larger`, `largerEq`, `smaller`, `smallerEq`, `unequal`.
     55 - Utils functions: `format`.
     56 
     57 
     58 ## Conversion
     59 
     60 Fractions can be converted to numbers and vice versa using the functions
     61 `number` and `fraction`. When converting a Fraction to a number, precision
     62 may be lost when the value cannot represented in 16 digits. 
     63 
     64 ```js
     65 // converting numbers and fractions
     66 const a = math.number(0.3)                       // number, 0.3
     67 const b = math.fraction(a)                       // Fraction, 3/10
     68 const c = math.number(b)                         // number, 0.3
     69 
     70 // loosing precision when converting to number: a fraction can represent
     71 // a number with an infinite number of repeating decimals, a number just
     72 // stores about 16 digits and cuts consecutive digits.
     73 const d = math.fraction('2/5')                   // Fraction, 2/5
     74 const e = math.number(d)                         // number, 0.4
     75 ```