Rational numbers can be expressed as fractions a/b where a and b are integers and b≠0.
a/b=0.1=1/10; a/b=0.11=11/100.
11/100-1/10=11/100-10/100=1/100. Divide this by 6: 1/600.
1st fraction: 1/10+1/600=60/600+1/600=61/600.
2nd fraction: 61/600+1/600=62/600=31/300.
3rd fraction: 63/600=21/200.
4th fraction: 64/600=8/75.
5th fraction: 65/600=13/120 (=66/600-1/600 or 11/100-1/600).
5 rational numbers are: 61/600, 31/300, 21/200, 8/75, 13/120.
Think of the two numbers 0.1 and 0.11 as end posts of a fence. We need to place 5 posts between the two end posts and space them equally. That means we have 7 posts altogether and there are 6 spaces between them. So we divide the distance between the posts by 6 then work out the position of each post.