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?

Answer 1

To convert the decimal \( x = 0.82 \) to a rational number, you would multiply both sides of the equation by 100. This is because the decimal has two digits after the decimal point.

Here’s how it looks:

\[ x = 0.82 \]

Multiplying both sides by 100 gives:

\[ 100x = 82 \]

Now, you can express \( x \) as a fraction:

\[ x = \frac{82}{100} \]

Then you can simplify that fraction if needed. In this case, both the numerator and denominator can be divided by 2:

\[ \frac{82}{100} = \frac{41}{50} \]

So, the decimal 0.82 can be expressed as the rational number \( \frac{41}{50} \).