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2/5 can be simply represented in the decimal system. It is 1 tenth of 20/5, ie 0.4 . But 1/3 is a bit more tricky, because if you say it is 1 tenth of 10/3 you get 3 and 1 left over to be divided by 3 so you've got nowhere. In the decimal system you can only represent 1/3 by 3/10 + 3/100 + 3/1000 etc forever. This is a geometric series, and the sum of this is (using the formula for a geometric series) just 0.3/(1-1/10) = 1/3 . That's a problem of numbers in "base 10". In base 3, one third is simply 0.1 . A number with repeating decimals (or groups of repeats) can always be turned back to a fraction by summing the series.
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What is the difference between non terminating decimals and repeating decimals?
You answered yourself in the question.
What is the difference between repeateing and terminating decimals?
A terminating decimal is something like .25, where a repeating decimal is something like 1/3
What is the difference between terminating and repeating numbers?
A terminating number has a definitive value - A repeating number continues indefinitely. For example - 10 divided by 8 is 0.125 (a terminating number) - 10 divided by 3 is 3.333333 (the decimal repeats indefinitely).
What is the differencce between a terminating and a repeating decimal?
A terminating decimal is a decimal that ends. A repeating decimal is a decimal that goes on and on.
What is the relationship between repeating decimals and fractions?
They are both representations of rational numbers.
