Question

Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?

Answer 1

Answer:

32

Step-by-step explanation:

Answer 2

The sum of the first $15$ digits is 32.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Let $x = 0.666666.....  

$x =  = 6/9  = 2/3

And  .606060.....  = 60/99

⇒(2/3) (60/99)

⇒ (2/99)(60/3)

⇒(2/99)(20)

⇒  40/99

⇒ .040404.........

So, the sum of the first 15 digits  = 8(4) + 7(0) + 0 = 32

Learn more about Arithmetic operations

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