Advertisements
Advertisements
Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.bar001`
Advertisements
Solution
Let `x = 0.bar001`
⇒ `x = 0.bar001 = 0.001001` ...(i)
On multiplying both sides of equation (i) by 1000, we get
1000x = 001.001......... ...(ii)
On subtracting equation (i) from equation (ii), we get
1000x – x = 001.001... – (0.001001...)
⇒ 999x = 001
∴ `x = 1/999`
APPEARS IN
RELATED QUESTIONS
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of `1/17`? Perform the division to check your answer.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Which of the following numbers can be represented as non-terminating, repeating decimals?
There are numbers which cannot be written in the form `p/q, q ≠ 0, p, q` both are integers.
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`5.bar2`
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.2555...
Express `0.6 + 0.bar7 + 0.4bar7` in the form `p/q`, where p and q are integers and q ≠ 0.
Write the following in decimal form and say what kind of decimal expansion has:
`4 1/8`
Write the following in decimal form and say what kind of decimal expansion has:
`2/11`
Write the following in decimal form and say what kind of decimal expansion has:
`329/400`
