Question

In the decimal expansion of 1/7000 the digit in the 7000th decimal place is

Answer 1

7000 ÷ 1 = 0.00014257
decimal place is 7/100000000=0.00000007
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Answer 2

Answer:

The required digit is 1

Step-by-step explanation:

$\frac{1}{7000}=0.00014285714285714.......$

If we can ignore three 0's after decimal point for a while then we can see that the 6 digits 142857 are getting repeated.

So, to find 7000th decimal place :

Step 1 : Subtract 3 from 7000 because of three 0's that are present just after the decimal point. So, 7000 - 3 = 6997

Step 2 : Now as we can see that after first three 0's the digits are repeated after every 6 digits so we divide 6997 by 6 and check the remainder

• When remainder is 1 digit is 1

• When remainder is 2 digit is 4

• When remainder is 3 digit is 2

• When remainder is 4 digit is 8

• When remainder is 5 digit is 5

• When remainder is 0 digit is 7

Step 3 : The remainder when 6997 is divided by 6 is 1.

So, In the decimal expansion of 1/7000 the digit in the 7000th decimal place is 1