Question

convert 0.8¯¯¯ to a rational number. calculator

Answer 1

To convert the repeating decimal \( 0.8\overline{8} \) to a rational number, we can follow these steps:

Let \( x = 0.8888\ldots \).

Now, multiply \( x \) by 10 to shift the decimal point one place to the right:

\[
10x = 8.8888\ldots
\]

Now, we have two equations:

1. \( x = 0.8888\ldots \)
2. \( 10x = 8.8888\ldots \)

Next, subtract the first equation from the second:

\[
10x - x = 8.8888\ldots - 0.8888\ldots
\]

This simplifies to:

\[
9x = 8
\]

Now solve for \( x \):

\[
x = \frac{8}{9}
\]

Thus, the rational number representation of \( 0.8\overline{8} \) is \( \frac{8}{9} \).