Convert the following repeating decimal to a fraction in simplest form.
point, 8, start overline, 5, end overline
.8
5
To convert the repeating decimal 0.885 to a fraction, we can use the following steps:
Let x = 0.885
Multiply x by 1000 to move the decimal point three places to the right:
1000x = 885.555...
Subtract x from 1000x to eliminate the repeating decimal:
1000x - x = 885.555... - 0.885
999x = 885
Divide both sides by 999 to solve for x:
x = 885/999
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 111:
x = 885/999
x = 885 ÷ 111 / 999 ÷ 111
x = 8 / 9
Therefore, the repeating decimal 0.885 can be written as the fraction 8/9 in simplest form.