# Rational and Irrational Numbers in Decimal Form

- Author:
- Lew W.S.

- Topic:
- Numbers, Rational Numbers

Explore rational numbers and irrational numbers here.
Rational numbers can be expressed in the form p/q where p, q are integers and q 0, and they may be terminating decimals or non terminating but repeating.
Irrational numbers are decimals which are non terminating and non repeating
For rational number 3/23 see that the digits 1304347826086956521739 is repeated, if we set the
the slider "number of digits in column to show" to 22 digits.
What happens if you change the slider value?
Try the rational number 2/17
Adjust the slider "number of digits in column to show" such that you can see the repetition of digits.
What are the digits repeated?
Explore the other rational numbers and irrational numbers!
For example, why some rational numbers have non terminating decimals (but with recurring or repeated digits) like 3/23 above while some have terminating decimals like 3/25 or 3/75, or 7/140 ?
Hint: Consider the denominator of the fraction in the lowest terms. What are the prime factors of the denominator?

ACKNOWLEDGEMENTS :
This applet originated from my request for help on the forum.
https://help.geogebra.org/topic/algorithm-for-rounding-to-n-decimal-places
Numerous people helped. Michael, Noel Lambert, Simona, Loco, chaffeur all offered ideas and samples. I am indebted to all of them.
See similar applets by Michael Borcherds at
https://www.geogebra.org/m/Uip
and Noel Lambert at
https://www.geogebra.org/m/vjgrefga
Updated on 19 Feb to correct display for terminating decimals and decimals greater than 1