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Actually ALL fractions are either terminating, or they are equivalent to repeating decimals.Try to carry out the long division, by hand, using ANY fraction; for example, 1/7. At each step, there will be a remainder. If this remainder happens to be zero, the division stops (the decimal is terminating).
However, if it doesn't stop, there can only be (in this example, when dividing by 7), six different options for the remainder; therefore, sooner or later, you MUST get a remainder that you already had before; therefore, the pattern repeats.
Note: The fractions (in simplest terms) that are equivalent to terminating decimals are exactly those which have a denominator whose only prime factors are 2 and 5. This is because those are the prime factors that make up the number 10 - the base of our decimal number system.
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Can fractions always be written as decimals?
You can always convert a fraction to a decimal. For some fractions, you'll get terminating decimals. For example, 1/8 = 0.125. For other fractions, you get repeating decimals, such as 1/7 = 0.142857 142857 142857...To convert the fraction to a decimal, just divide the numerator by the denominator, for example on a calculator.
What is terminating and repeating in math?
They're applied to decimals. Some decimals stop, like 0.75 That's a terminating decimal. Some decimals keep on going in patterns, like 0.3333... or 0.565656... Those are repeating decimals.
Why are there repeating decimals?
Some numbers cannot be written exactly and their decimals repeat infinitely. The best example is 1/3 written as a decimal. It is 0.33333 going on infinitely. Some have multiple digits that keep repeating.
What is a non terminating decimal called?
Some non-terminating decimals are repeating decimals.
What does non terminating non repeating mean?
Some decimals terminate. (0.3) Some decimals repeat (0.3333333) Some do neither. Pi is the most famous example. 3.1415 etc.
