Rational Numbers in Different Forms Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

View previous attempt
Question
To convert 0.82¯¯¯¯¯
to a rational number, you would set x
equal to 0.82¯¯¯¯¯
and then multiply both sides of the equation by what number?(1 point)

Answer 1

To convert the repeating decimal \( 0.82\overline{82} \) (which we can represent as \( x = 0.828282... \)) to a rational number, we follow these steps:

1. Set \( x = 0.828282... \).

2. To eliminate the repeating part, we multiply both sides of the equation by 100. This is because the repeating part has two digits (82), so we need to shift the decimal point two places to the right.

Thus, multiplying both sides by 100 gives us:

\[ 100x = 82.828282... \]

This sets us up to subtract the original equation from this one, allowing us to eliminate the repeating part.

So the answer to your question is: 100.