Accuracy of Fractions vs Decimals: Why Decimals?

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SUMMARY

The discussion highlights the advantages of using decimals over fractions in mathematical representation. While fractions like 1/3 provide a more accurate representation of certain values, decimals simplify addition and subtraction processes. Additionally, many numbers, such as π, cannot be accurately expressed as fractions. Decimals also convey the precision of measurements, indicating that 0.3 is less accurate than 0.33.

PREREQUISITES
  • Understanding of basic arithmetic operations (addition and subtraction)
  • Familiarity with fractions and decimals
  • Knowledge of mathematical concepts of accuracy and precision
  • Basic comprehension of irrational numbers, such as π
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  • Research the mathematical properties of fractions and decimals
  • Explore the significance of precision in numerical representation
  • Learn about the implications of using irrational numbers in calculations
  • Investigate the historical development of the decimal system
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Mathematicians, educators, students, and anyone interested in understanding the practical applications of numerical systems in everyday calculations.

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For exmaple you can represent one third more accurately with fractions (1/3) than with decimals (.33 etc etc). So why do we use the decimal system ?
 
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Not really stupid,

the basic reason is addition and subtraction are much easier with decimals. And of course many numbers aren't representable by fractions such as π
 
Further, when we use fractions, it implies we know the value to an infinite accuracy. In real life, this is not practical. The decimal is useful, as it records the accuracy of the figure as well. Ie. we know 0.3 is a less accurate measurement than 0.33.
 

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