Right, but note that it is displaying a truncated form of the number in the output cell: all digits are still there.

To adjust how much you want displayed go to the Preferences. Under the Appearance tab go to the Numbers tab, and under that go to theFormatting tab. You can adjust the Displayed Precision in the indicated input field (it is set at default to 6)

The full number is still saved in your variable. The default setting for the output foreign is to only display a fixed number of digits of the expression.

If you execute

InputForm[a]

You will see that your original expression is still there.