ANSWER
Five natural numbers.
EXPLANATION
The given inequality is
[tex] \frac{1}{7} \: < \: \frac{n}{10} \: < \: \frac{4}{5} [/tex]
We multiply each term in the inequality by 10 to obtain,
[tex] \frac{1}{7} \times 10\: < \: \frac{n}{10} \times 10\: < \: \frac{4}{5} \times 10[/tex]
This gives us,
[tex] \frac{10}{7} \: < \: n \: < \: \frac{40}{5} [/tex]
We simplify further to obtain,
[tex] 1\frac{3}{7} \: < \: n \: < \: 8[/tex]
The natural numbers that satisfy the inequality are;
[tex]2,3,4,5,7[/tex]
Hence 5 natural numbers satisfy the given inequality.
