No, pi is not a repeating decimal.
Pi (π) is an irrational number, which means it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Its decimal representation is non-terminating (it goes on infinitely) and non-repeating (the digits do not fall into a repeating pattern).
Understanding Repeating Decimals
A repeating decimal, also known as a recurring decimal, has a block of digits that repeats infinitely. For example:
- 1/3 = 0.3333... (the digit 3 repeats)
- 1/7 = 0.142857142857... (the block "142857" repeats)
Repeating decimals can always be expressed as fractions.
Why Pi is Different
Pi, on the other hand, has a decimal expansion that continues infinitely without any repeating pattern. Its approximate value is 3.14159265359..., but this is just a truncated representation. The digits continue indefinitely in a seemingly random order.
Key Characteristics of Pi
- Irrational: Cannot be expressed as a fraction of two integers.
- Transcendental: Not the root of any non-zero polynomial equation with rational coefficients. (This is a stronger condition than being irrational).
- Non-terminating: Its decimal representation goes on forever.
- Non-repeating: Its decimal representation does not have a repeating pattern.
Because pi is a non-repeating, non-terminating decimal, it is classified as an irrational number.
