Question

Find the sum of the irrational numbers : 0.101001000100001… and 0.010110111011110… . If it
is a rational number, write it in the integer- by-integer form.

Answer 1

Answer:

Let x = 0.1010010001… and y = 0.0101101110… . Then

x + y = 0.1010010001… + 0.0101101110…= 0.111111… = 0.1.

Since x + y has a non-terminating but repeating decimal expansion, x + y is a rational number. Let the rational number be a. Then a = 0.11111…

Multiplying by 10, we get 10a = 1.1111…

∴ 10a − a = 1.1111… − 0.1111 = 1.0000…. or 9a = 1 or a = 1/9

∴ x + y = 1/9

Step-by-step explanation:

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