Finding the p/q form of repeating decimal numbers, where p and q are integers and q≠0. class 9 ncert
Answers
Answer: This is the method:
Step-by-step explanation:
Let me explain with an example.
Take the repeating decimal number 2.33333.......
To represent the given number in p/q form where q ≠ 0, follow the given steps:
1) Let x = 2.3333......
2) Multiply both sides with 10. You may change this number to any power of 10 as per the length of the reapeating string of numbers after the decimal. Since only one number i.e. 3 is being repeated we take 10. On doing so you will get:
10x = 23.3333......
3) Observe the RHS. Here 23.333.... can be written as 21 + 2.333... . Moreover, 2.333... = x (as in step 1).
4) Now RHS can be written as 21+x (from the above step).
5) Modify your first equation:
10x = 21 + x
=> 10x - x = 21
=> 9x = 21
=> x = 21/9
=> x = 7/3 (On reducing to lowest term).
Therefore, 2.333... = 7/3