I think most of you all agree with me that as teenagers (way back in 70’s and 80’s) we did nothing in math beyond our textbooks. Teaching of Mathematics was restricted to formulae and problem solving. Though I did enjoy solving problems because of my passion with the subject, but I have to admit that I lacked clarity in conceptual knowledge.
With the introduction of CCE (Continuous Comprehensive Evaluation) by CBSE the practical side of the subject was explored even more by Math teachers. Truly I have to admit that the Pandora’s Box has opened to answer many conceptual queries. Even though CBSE has given up on CCE due to various reasons, it certainly made the teachers explore the subject.
In this post lets see some interesting patterns in Decimal representation of some fractions
From the above table we observe that when the denominator is a power of 2, then its decimal represents power of 5 (and vice versa) taking the number of decimal places equal to its power.( of course using the rule)
Thus if the above rule is made clear to the students also solve using the above technique
Few more interesting decimal patterns
Consider a unit fraction with Prime denominator.
In most cases the periodicity is 1 less than the prime number or the periodicity is a factor of the number which is 1 less than the prime number.
If the denominators are prime this conjecture can be used.
rule)
