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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.

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Q: What causes the difference in terminating decimals and repeating decimals?
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What causes the difference between terminating and repeating decimals?

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.


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.


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.


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 does the arrangement of atoms in a repeating pattern in a mineral causes the formation?

of crystals.


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the presence of minerals such as sodium cholride,magnesium etc causes the difference in ocean water ....


Will hearing the same question over and over again cause anger?

Sometimes yes, it causes a lot of anger in people. Repeating and listening same thing again causes frustration.


What causes the difference between breccias and conglomerante?

The difference between breccias and conglomerate is that breccias are angular and conglomerates are smooth. What causes rocks to be smooth is transportation, such as when rocks are in a stream and are worn down. Therefore transportation is what causes the difference between breccias and conglomerates.


What format causes thecells to displaywith two decimals?

FORMAT / Format Cells / Number tab / Number / 'Decimal places' window / fill in '2'.


In an electrical circuit a voltage difference is?

Volt difference causes a short circuit! ChaCha


What causes difference in movement?

The steering wheel was turned.