Any easy way to find the values of fractions?

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Discussion Overview

The discussion revolves around methods for finding the decimal values of fractions, particularly those with denominators that end in '9', without using a calculator. Participants explore various techniques and share their experiences with different approaches.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant inquires about easy methods to determine the value of fractions like \(\frac{1}{19}\) without a calculator.
  • Another participant suggests that if the denominator is a divisor of a number of the form 99...900..0, there are straightforward methods to find the decimal representation, providing examples such as \(\frac{7}{33} = 0.21212121...\).
  • A different participant states that the value of \(\frac{1}{19}\) is simply \(\frac{1}{19}\), implying a lack of further simplification.
  • One participant mentions that they find long division to be a fast and easy method for determining the decimal representation of fractions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a singular method for finding decimal values of fractions, and multiple approaches are presented without resolution on which is preferable.

Contextual Notes

Some methods discussed depend on specific properties of the denominators, and there may be limitations in the applicability of these methods to all fractions with denominators ending in '9'.

Who May Find This Useful

Individuals interested in mathematical techniques for converting fractions to decimal form, particularly those who prefer non-calculator methods.

rock.freak667
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For example..without a calculator is there any easy way to find the value of \frac{1}{19} or any fraction in which the denominator ends in a '9' ?
 
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Not that I know of. If the denominator is a divisor of a number of the form 99...900..0 then there is an easy way. For example:
7/33 = 21/99 = 0.21212121...
2/55 = 36/990 = 0.036363636...
8/3700 = 216/99900 = 0.00216216216...
 
The value of 1/19 is...1/19.
 
rock.freak667 said:
For example..without a calculator is there any easy way to find the value of \frac{1}{19} or any fraction in which the denominator ends in a '9' ?
To find the decimal representation of a fraction, I find long division to be pretty fast and easy...
 

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