Advertisements
Advertisements
प्रश्न
Express the following in the form `p/q`, where p and q are integers and q ≠ 0.
`0.bar6`
Advertisements
उत्तर
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
संबंधित प्रश्न
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.]
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?
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:
0.888...
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`5.bar2`
Show that 0.142857142857... = `1/7`
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:
`3/13`
Write the following in decimal form and say what kind of decimal expansion has:
`2/11`
