nishikaapoona
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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?

Respuesta :

sqdancefan

Answer:

  [tex]32\text{ for }x=0.\overline{40}[/tex]

Step-by-step explanation:

It looks like you want the sum of digits of the product ...

  [tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]

Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:

  sum = 8×4 +7×0 = 32

The sum of the first 15 digits after the decimal point is 32.

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