Advertisements
Advertisements
Question
Write the following in decimal form and say what kind of decimal expansion has:
`2/11`
Advertisements
Solution
Dividing 2 by 11, we get
`11)overline2.0000(0.1818......`
−11
90
−88
20
−11
90
−88
2
Here, the repeating block of digits is 18.
∴ `2/11` = 0.1818...
= `0.overline18`
Thus, the decimal expansion of `2/11` is non-terminating repeating.
APPEARS IN
RELATED QUESTIONS
You know that `1/7=0.bar142857.` Can you predict what the decimal expansions of `2/7, 3/7, 4/7, 5/7, 6/7` are, Without actually doing the long division? If so, how?
[Hint: Study the remainders while finding the value of `1/7` carefully.]
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.
Look at several examples of rational numbers in the form `p/q` (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Write three numbers whose decimal expansions are non-terminating non-recurring.
Which of the following numbers can be represented as non-terminating, repeating decimals?
If `sqrt(2) = 1.4142`, then `sqrt((sqrt(2) - 1)/(sqrt(2) + 1))` is equal to ______.
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.bar001`
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:
`1/11`
Write the following in decimal form and say what kind of decimal expansion has:
`3/13`
