Multiple Decimal Expansions: Explained

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SUMMARY

Multiple decimal expansions exist for certain numbers, particularly terminating decimals. For example, the number 1 can be represented as both 1.0 and 0.999..., demonstrating that different decimal forms can represent the same value. This phenomenon is confirmed in discussions on Physics Forums and detailed in the Wikipedia article on repeating decimals. Understanding this concept is crucial for grasping the nuances of decimal representation in mathematics.

PREREQUISITES
  • Understanding of decimal numbers and their representations
  • Familiarity with the concept of terminating and repeating decimals
  • Basic knowledge of mathematical equivalence
  • Awareness of mathematical notation and terminology
NEXT STEPS
  • Research the properties of terminating and repeating decimals
  • Explore the concept of limits in relation to decimal expansions
  • Learn about the implications of decimal representation in real analysis
  • Investigate the historical context of decimal notation and its evolution
USEFUL FOR

Mathematicians, educators, students in mathematics, and anyone interested in the intricacies of number representation and decimal systems.

Swetasuria
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I read here in Physics Forums that a number can have more than one decimal expansion.

Really? Can someone explain how?

Is it that any number can have more than one decimal expansion or only some numbers?
 
Last edited:
Mathematics news on Phys.org
See the 0.9... article on Wikipedia or the https://www.physicsforums.com/showpost.php?p=3357236&postcount=1 on this forum.
 
Swetasuria said:
I read here in Physics Forums that a number can have more than one decimal expansion.

Really? Can someone explain how?

Is it that any number can have more than one decimal expansion or only some numbers?

Hi Swetasuria. You can take the "usual" decimal expansion of any terminating decimal and replace the last digit with one smaller, then add repeating 9's after that, and yes it's the same number. :smile:
 

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