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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.
How do you turn a division into a decimal fraction?
You do a long division, adding decimal digits until you get a remainder of zero (terminating decimal) or a repeating pattern of decimal digits.
If the results of long division repeat without ending the guotient is a?
It is a repeating decimal.
How do you use long division to find a repeated decimal equivalency for 89?
89 is an integer, not a fraction. The repeated decimal equivalents are 89.000....(repeating) or 88.999... (repeating).
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 know when a number is a repeating decimal?
If, when you carry out long division, the remainder at some stage happens to be the same as the remainder at an earlier stage.
What does seven fifteenths equal in a decimal with work?
Seven divided by fifteen equals 0.4666 repeating. Write it out as a long division problem.
What is 434 divided by 7?
62
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).
Do rational numbers have a repeating decimal?
They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.
What is 4 divided by 1350?
0.003
What is 8 divided by 288 in long division?
0.0278
What is 9875 divided 6 in long division?
1645.8333
