show that 0.142857142857...=1/7
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Answered by
100
Answer:
1/7
Step-by-step explanation:
Let x = 0.142857142857 …………………..(i)
On multiplying both sides of Eq. (i) by 1000000, we get
1000000 x = 142857.142857…………………………(ii)
On subtracting Eq. (i) from Eq. (ii), we get
1000000 x – x = (142857.142857…) – (0.142857..) ⇒ 999999 x = 142857
∴ x = 142857/999999 = 1/7
Hence proved.
Answered by
22
Answer:
1/7
Step-by-step explanation:
Let x = 0.142857142857 …………………..(i)
On multiplying both sides of Eq. (i) by 1000000, we get
1000000 x = 142857.142857…………………………(ii)
On subtracting Eq. (i) from Eq. (ii), we get
1000000 x – x = (142857.142857…) – (0.142857..) ⇒ 999999 x = 142857
∴ x = 142857/999999 = 1/7
Hence proved.
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