Question

To convert 0.264 to a rational number, you would set x
equal to 0.264 and then multiply both sides of the equation by what number?

Answer 1

To convert the decimal \( 0.264 \) to a rational number, you would set \( x = 0.264 \) and then multiply both sides of the equation by \( 1000 \) because \( 0.264 \) has three decimal places.

Here’s how it works:

1. Set \( x = 0.264 \).
2. Multiply both sides by \( 1000 \):

\[
1000x = 1000 \cdot 0.264
\]
\[
1000x = 264
\]

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

\[
x = \frac{264}{1000}
\]

4. You can simplify this fraction if needed, but \( \frac{264}{1000} \) is a rational number.

So, you would multiply both sides by \( 1000 \).