Lösung 1.1:7a

If we multiply 3.14 by 100 the decimal point will move two places to the right, i.e.

\displaystyle 100\cdot 3\textrm{.}14 = 314

and dividing both sides by 100 we see that

\displaystyle 3\textrm{.}14 = \frac{314}{100}\,\mbox{.}

This shows that 3.14 can be written as the quotient of two integers which means it is a rational number.