Any easy way to find the values of fractions?

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Finding the decimal values of fractions, particularly those with denominators ending in '9', can be challenging without a calculator. An effective method involves recognizing that if the denominator is a divisor of numbers like 99...900..0, the decimal can be derived easily. For instance, fractions such as 7/33 and 2/55 can be converted to repeating decimals by manipulating their forms. Long division is also highlighted as a quick and straightforward technique for determining decimal representations of fractions. Ultimately, while specific patterns exist, the value of 1/19 remains as is without a simple conversion method.
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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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