Terminating Decimals Calculator
MathFind the decimal value of a fraction and check whether it terminates or repeats.
Decimal Value
The fraction expressed as a decimal (repeating decimals are shown rounded).
Does It Terminate?
Whether the decimal has a finite number of digits (terminates) or repeats forever. Yes, this fraction terminates.
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
What makes a decimal terminate versus repeat?
A fraction in lowest terms produces a terminating decimal exactly when its denominator's only prime factors are 2 and 5, the prime factors of 10. Any other prime factor in the denominator (like 3, 7, or 11) causes the decimal to repeat forever.
What is an example of each?
12/15 simplifies to 4/5, and since 5 is a factor of 10, this terminates as 0.8. 10/3 stays as a denominator of 3, which is not a factor of 10, so it repeats forever as 3.333...
How is this checked without doing long division?
After simplifying the fraction to lowest terms, repeatedly divide the denominator by 2 and then by 5. If the denominator is reduced all the way down to 1, the decimal terminates; if any other factor remains, it repeats.
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