The denominator is 2 cubed times 5, which equals 40. Since the highest power between the prime factors 2 and 5 is 3, the terminating decimal expansion will have exactly 3 decimal places.
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First, find a common denominator for 1/6 and 2/5, which is 30, giving 5/30 and 12/30. The five rational numbers lying between them are 6/30, 7/30, 8/30, 9/30, and 10/30.
To find 6 rational numbers between 3 and 4, convert them into fractions with a denominator of 7, giving 21/7 and 28/7. The intermediate numbers are 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.
To find 5 rational numbers between 2/5 and 3/5, multiply the numerator and denominator of both fractions by 6. This gives 12/30 and 18/30. The intermediate rational numbers are 13/30, 14/30, 15/30, 16/30, and 17/30.
Another effective method is the midpoint formula, where you add the two rational numbers together and divide by 2. Repeating this averaging process will continually generate new rational numbers between them.