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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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What causes a repeating decimal in the long division algorithm?
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.
How do you 4 divided by 7 as a decimal?
You do a long division - using whichever method you have been taught. Don't stop with a remainder but carry on until you see a repeating pattern emerging (after 6 decimal places).
What is the process of changing a fraction to a decimal or to a percentage?
The answer depends on the form of the fraction. If it is a decimal fraction, you need to nothing to convert it to a decimal! (?). If it is in the form of a rational fraction, you need to use long division to divide the numerator by the denominator. The division will either come to an end or will go into a repeating loop of digits. The quotient from the division is the decimal equivalent. To convert to a percentage, simply move the decimal point two places to the right - inserting os if required.
How do you convert a fraction to decimal?
Carry out long division.
How do you write A to B as a decimal?
You use long division of A by B.
