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Math

Percentages

A percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number. This project includes a proper abstraction: Percentage.

The easier way to create a percentage is to send the message percent to a number. For example 5 percent will create an object representing 5%. There are two common cases also covered as instance creation methods (0% and 100%):

Percentage zero. "0%"
Percentage oneHundred "100%"

Percentages can also be created providing a ratio:

Percentage ratio: 1. "100%"
Percentage ratio: 1/2 "50%"

These percentages can be operated arithmetically with any number or other percentages. Try printing the following expressions:

20 percent * 5. "1"
10 percent + 105 percent. "115%"
10 percent + 15.0 "15.1"

Percent changes applied sequentially do not add up in the usual way. For example, if we apply a 10% increase to a value (200), it will raise it to 220. If we apply later a 10% decrease to it (a decrease of 22), the final value will be 198, not the original 200. The reason for the apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different quantities (200 and 220, respectively), and thus do not "cancel out". This can be handled easily:

(200 increasedBy: 10 percent) decreasedBy: 10 percent "198"

Per Mille

Is similar to a percentage but expressed as a fraction of 1000. The easier way create one is to send the message perMille to a number.

6 perMille. "6‰"
12 perMille "12‰"

Number Extensions for GS64

  • isZero returns true if the receiver equals 0
  • nthRoot: returns the nth root of the receiver
  • round: round the decimal part of the receiver to be limited to the desired number of decimal digits

Float Extensions for GS64

  • isInfinite returns true if the receiver is infinite

Integer Extensions for GS64

  • #printStringHex prints the receiver in hexadecimal
  • #printStringLenght:padded: prints the receiver to a minimum size, optionally padding with zeros.
  • readFrom:ifFail: parses an Integer or evaluates the failure block if the format is invalid.

Some definitions and examples are based on the ones on Wikipedia