Advertisements
Advertisements
Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0.
`0.bar6`
Advertisements
Solution
Let `x = 0.bar6`
x = 0.66666....... ...(1)
Multiplying equation (1) by 10 on both side
10x = 6.66666
10x = 6 + 0.666 ...[From equation (1)]
10x = 6 + x
10x - x = 6
9x = 6
`x = 6/9`
∴ `0.bar6 = 2/3`
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.]
Express 0.99999 .... in the form `p/q`. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
The value of 1.999... in the form `p/q`, where p and q are integers and q ≠ 0, is ______.
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.2
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.888...
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.bar001`
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.1bar34`
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.404040...
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:
`2/11`
