How many different numbers between 1/8 and 1/2, inclusive, can be displayed on your shiny new 8-digit calculator?

We start with 1/8: | .1 2 5 0 0 0 0 0 | |

Then we have | .1 2 5 | where there are 10 possible digits for each blank, thus 10^{5} possible numbers starting with .125 |

Similarly for | .1 2 6 , .1 2 7 , .1 2 8 , and .1 2 9 |
We have 5 x 10^{5} so far. |

Now, for | .1 3 _ _ _ _ _ _, .1 4 _ _ _ _ _ _, .1 5 _ _ _ _ _ _, .1 6 _ _ _ _ _ _, .1 7 _ _ _ _ _ _, .1 8 _ _ _ _ _ _, and .1 9 _ _ _ _ _ _ |
we’ll get 7 x 10^{6} more. |

And for | .2 _ _ _ _ _ _ _, .3 _ _ _ _ _ _ _, and .4 _ _ _ _ _ _ _ |
we’ll get 3 x 10^{7} more. |

Finally we have | .5 |

So we add: (5 x 10^{5}) + (7 x 10^{6}) + (3 x 10^{7}) + 1 = 37,500,001. That’s a lot.