Express 8/27 as a repeating decimal. * 1 point 0.2962929292929... 2.96969696969... 0.29666666666... 0.296296296296... 0.2222999996666...

Answer 1

To express \( \frac{8}{27} \) as a decimal, we can perform long division.

When we divide 8 by 27, we find:

1. \( 27 \) goes into \( 80 \) (after adding a decimal point and a zero) \( 2 \) times (since \( 27 \times 2 = 54 \)).

   • This gives us \( 80 - 54 = 26 \).
   • Bring down a zero to make it \( 260 \).

2. \( 27 \) goes into \( 260 \) \( 9 \) times (since \( 27 \times 9 = 243 \)).

   • This gives us \( 260 - 243 = 17 \).
   • Bring down a zero to make it \( 170 \).

3. \( 27 \) goes into \( 170 \) \( 6 \) times (since \( 27 \times 6 = 162 \)).

   • This gives us \( 170 - 162 = 8 \).
   • Bring down a zero to make it \( 80 \) again.

Now we can see that the decimal starts to repeat. The sequence of digits \( 296 \) will continue to repeat.

So, \( \frac{8}{27} \) as a repeating decimal is:

\[ 0.\overline{296} \]

From the options given, the correct answer is:

0.296296296296...