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प्रश्न
Show that 0.142857142857... = `1/7`
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उत्तर
Let x = 0.142857142857 ...(i)
On multiplying both sides of equation (i) by 1000000, we get
1000000x = 142857.142857 ...(ii)
On subtracting equation (i) from equation (ii), we get
1000000x – x = (142857.142857...) – (0.142857...)
⇒ 999999x = 142857
∴ `x = 142857/999999 = 1/7`
Hence proved.
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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.]
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.
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.
The decimal expansion of the number `sqrt(2)` is ______.
The value of 1.999... in the form `p/q`, where p and q are integers and q ≠ 0, is ______.
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