Full Precision Calculator
Full Precision Calculator
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What is 17 divided by 53 as a decimal?
What if we used a calculator?
iPhone Calculator (vertical)
gives you 8 digits after
the decimal point
iPhone Calculator (horizontal)
gives you 15 digits after the decimal point
TI-34 Calculator gives you xx digits after the decimal point
Google gives you 11 digits after the decimal point
Are any of these answers correct?
Practically speaking,
YES
Mathematically speaking,
NO
Why?
=
Terminate or Repeat
Terminate or Repeat
Given any rational number as a fraction or mixed number, we tell if that rational number is going to "terminate" or "repeat" when written as a decimal. How?
Simplify the rational number to its simplest form.
Find out the prime factorization of the denominator.
As a decimal, the number will:
Terminate if the unique prime factors of the denominator are 2, 5, or both 2 and 5.
Repeat if the unique prime factors of the denominator include any other prime number (other than 2 or 5).
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