Mathematical Introduction for Physics and Engineering

by Samuel Dagan (Copyright © 2007-2020)

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Show that any number expressed in decimal form with finite number of digits, is a rational number!**

Any number expressed in decimal form with finite number of digits can be written in the form of

$$I\times {10}^{n}\text{\hspace{1em}}\text{or}\text{\hspace{1em}}I\times {10}^{-n}$$where *I* is an integer and *n* is a non negative integer.

On the lefthand side there is a product of two integers, which is rational.

On the righthand side there is a ratio between two integers with non vanishing denominator, which is also rational.
## Score

There are different ways to present the solution of this exercise.

Any solution that is correct and covers all possible numbers expressed in decimal form with finite number of digits entitles the user to 10 points.

Any other solution is worth nothing.