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
0 votes
7.4k views
in Mathematics by (15.0k points)

Express 0.99999.... in the form p/q. Are you surprised by your answer? Discuss why the  answer makes sense with your teacher and classmates.

1 Answer

0 votes
by (24.9k points)
selected by
 
Best answer

Let x = 0.99999......... ......(a)

We need to multiply both sides by 10 to get

10x = 9.9999...... ....(b)

We need to subtract (a) from (b). to get

We can also write 9 x = 9 as x = 9/9 or x = 1.

Therefore, on converting 0.99999.... in the p/q form, we get the answer as1.

Yes at a glance we are surprised at our answer. But the answer makes sense when we observe that 0.9999……… goes on forever. SO there is not gap between 1 and 0.9999……. and hence they are equal.

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

...