Look at several examples of rational numbers in the form $\frac{p}{q}$ (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?

Question

Look at several examples of rational numbers in the form  $\frac{p}{q}$  (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?

cdquestions Admin · Accepted Answer

Terminating decimal expansion will occur when denominator q of rational number  $\frac{p}{q}$  is either of 2, 4, 5, 8, 10, and so on…  $\frac{9}{4}$  = 2.25 $\frac{11}{8}$  = 1.375 $\frac{27}{5}$  = 5.4 It can be observed that terminating decimal may be obtained in the situation where prime factorisation of the denominator of the given fractions has the power of 2 only or 5 only or both.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Look at several examples of rational numbers in the form \(\frac{p}{q}\) (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 and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions