Q.6. Look at several examples of rational numbers in the form $\frac{\mathrm{p}}{\mathrm{q}}$ (q≠0) where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Solution:

If the prime factorisation of the denominator of the given fractions has the power of 2 only or 5 only or both (and no other factors), the decimal expansion will be terminating.

For example,

$\frac{1}{2}$ = 0.5, denominator q = 21

$\frac{7}{8}$ = 0.875, denominator q = 23

$\frac{4}{5}$ = 0.8, denominator q = 51

$\frac{1}{3}$ = 0.3333… (denominator contains factor 3)