I want to know if there are numbers in the interval $[\frac{28}{100},\frac{29}{100}]$
which have a $7$ in their decimal expansion.
I would say "yes", because we can write $0.28=0.2799999999...$
But this is the only number in this interval, right?
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6$0.287$ is another. – David Mitra May 12 '15 at 10:53
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Yes, though David Mitra is right. But I can't understand, what you mean to do by finding such numbers? – Sufyan Naeem May 12 '15 at 10:55
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There are infinite numbers in your interval, and infinite of them have a $7$ in their decimal expansion. All the numbers that start with $0.28$ in decimal notation, followed by anything that contains a $7$, satisfy your requirement.
Examples: $0.287$, $0.2807$, $0.2817$, $0.2871$, $0.280000000000000007$
Notice that this is not limited to the rationals. For example
$0.28 + e/1000$
also satisfies the required condition.
jordix
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