Sarthaks Test
0 votes
668 views
in Real Numbers by (49.1k points)
closed by

Without actual division, find which of the following rational numbers have terminating decimal expansion. 

(i) \(\frac{7}{128}\)

(ii) \(\frac{21}{15}\)

(iii) \(\frac{219}{2200}\)

1 Answer

+1 vote
by (48.7k points)
selected by
 
Best answer

(i) \(\frac{7}{128}\)

So \(\frac{7}{128}\) = \(\frac{7}{2^75^0}\)

This of the form 4m, n ∈ W 

So \(\frac{7}{128}\) has a terminating decimal expansion

(ii) \(\frac{21}{15}\)

So \(\frac{21}{15}\) has a terminating decimal expansion.

(iii) \(\frac{219}{2200}\)

\(\frac{219}{2200}\) = \(\frac{219}{2^35^211^1}\)

∴ This is not of the form \(\frac{p}{2^m5^n}\)

So \(\frac{219}{2200}\) has a non-terminating recurring decimal expansion.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...