Decimals on Calculator Screen

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


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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 105 possible numbers starting with .125
Similarly for .1 2 6          ,
.1 2 7          ,
.1 2 8          , and
.1 2 9          
We have 5 x 105 so far.
Now, for .1 3 _ _ _ _ _ _,
.1 4 _ _ _ _ _ _,
.1 5 _ _ _ _ _ _,
.1 6 _ _ _ _ _ _,
.1 7 _ _ _ _ _ _,
.1 8 _ _ _ _ _ _, and
.1 9 _ _ _ _ _ _
we’ll get 7 x 106 more.
And for .2 _ _ _ _ _ _ _,
.3 _ _ _ _ _ _ _, and
.4 _ _ _ _ _ _ _
we’ll get 3 x 107 more.
Finally we have .5

So we add: (5 x 105) + (7 x 106) + (3 x 107) + 1 = 37,500,001. That’s a lot.

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