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'decimal fraction'
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| Title of object: |
decimal fraction |
| Canonical Name: |
DecimalFraction |
| Type: |
Definition |
| Created on: |
2007-08-06 11:10:48 |
| Modified on: |
2007-08-06 11:10:48 |
| Classification: |
msc:11-01 |
Preamble:
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Content:
A rational number $r$ is called a \emph{decimal fraction} if for some non-negative integer $k$, $10^kr$ is an integer. For example, any integer, as well as rationals such as $0.23123$, $3/4$ are all decimal fractions. Rational numbers such as $1/3$, $7/13$ are not.
There are two other ways of characterizing a decimal fraction: for a rational number $r$,
\begin{itemize}
\item $r$ is a decimal fraction
\item $r=\displaystyle{\frac{p}{q}}$ where $p$ and $q$ are integers, and $q=2^m5^n$ for some non-negative integers $m$ and $n$
\item $r$ has a terminating decimal expansion.
\end{itemize} |
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