9464

Rounding p-adic Rationals

Rational -adic numbers share the same decimal notation and math as do repeating decimals. A vinculum (or overbar) is also allowed in -adic number notation to indicate repeated digits. However, a nonzero vinculum must appear only on the leftmost digits, while normal repeating decimals use a vinculum only on the right. This Demonstration rounds to only repeating digits.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

In this Demonstration, -adic rounding is accomplished by truncating repeating digits of on the left. This is equivalent to replacing the integer part of with , where is the floor function.
There is a one-to-one mapping between the two notations for the rational numbers, but in what sense can truncation be considered rounding for -adic numbers? Multiplying the -adic rational notation by the value of the denominator we see something like the numerator. This is a useful motivation for students being introduced to the -adic norm.
The in -adic stands for prime. A -adic system is defined by which prime is chosen to be . This Demonstration allows "10-adic" numbers. Although 10-adic is not a proper -adic system, it does behave like a -adic representation of the rational numbers. The 10-adic option is included because students are familiar with base 10 numbers.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+