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When you divide by a divisor q, the remainders can only be integers that are smaller than q. If the remainder is 0 then the decimal is terminating. Otherwise, it can only take the values 1, 2, 3, ... ,(q-1). So, after at most q-1 different remainders you must have a remainder which has appeared before. That is where the long division algorithm loops back into an earlier pattern = repeating sequence.

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Q: What causes a repeating decimal in the long division algorithm?
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What causes a repeating decimal in the long division?

When you divide by a divisor q, the remainders can only be integers that are smaller than q. If the remainder is 0 then the decimal is terminating. Otherwise, it can only take the values 1, 2, 3, ... ,(q-1). So, after at most q-1 different remainders you must have a remainder which has appeared before. That is where the long division algorithm loops back into an earlier pattern = repeating sequence.


What causes the difference in terminating decimals and repeating decimals?

If a fraction is a rational number then if the denominator goes into the numerator or into the numerator multiplied by a power of 10, then you will have a terminating decimal. Otherwise it will be a repeating decimal.


What causes repeating decimals to happen?

If the denominator in the simplest form of a rational number has any prime factor other that 2 or 5 then it will not divide the numerator without remainder. This results in a repeating decimal.


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If the condition has been reached.


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of crystals.


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specialization among workers


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Hyperplasia.


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The division of labor causes each worker to perform a different and unique task.


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excess cell growth and division