Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
2.8k views
in Number System by (37.9k points)
closed by

Write the following rational numbers in their decimal form and also state which are terminating and which have non-terminating repeating decimals.

i) \(\frac{3}{8}\)

ii) \(\frac{229}{400}\)

iii) 4\(\frac{1}{5}\)

iv)\(\frac{2}{11}\)

v) \(\frac{8}{125}\)

1 Answer

+2 votes
by (36.5k points)
selected by
 
Best answer

i) \(\frac{3}{8}\)

[!! Denominator 8 = 23, consists of only 2’s. Hence a terminating decimal.] 

\(\frac{3}{8}\)= 0.375 is a terminating decimal.

ii) \(\frac{229}{400}\)

[!! Denominator 400 = 24 × 52 = 2n × 5m . Hence a terminating decimal.] 

\(\frac{229}{400}\)= 0.5725 is a terminating decimal.

iii) \(4\frac{1}{5}\)

\(4\frac{1}{5}\) = 4 + \(\frac{1}{5}\)

[!! Denominator is 5. Hence a terminating decimal.] 

∴ 4\(\frac{1}{5}\) = 4.2 is a terminating decimal.

iv) \(\frac{2}{11}\)

[!! Denominator is not of the form 2m × 5n . Hence a non-terminating repeating decimal.] 

\(\frac{2}{11}\)\(0.\overline{18}\) is a non terminating, repeating decimal.

v) \(\frac{8}{125}\)

[!! Denominator 125 = 53 . Hence a terminating decimal.] 

\(\frac{8}{125}\)= 0.064 is a terminating decimal.

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

...