Question
To convert 0.264 repeating number to a rational number, you would set x equal to 0.264 and then multiply both sides of the equation by what number? (1 point)
10
999
1,000
100
10
999
1,000
100
Answers
GPT-4o mini
To convert the repeating decimal \( 0.264\overline{264} \) to a rational number, you would set \( x = 0.264264264\ldots \).
Since the repeating part "264" has 3 digits, you would multiply both sides of the equation by \( 1000 \) (not 10 or 100), as this will shift the decimal point three places to the right.
Thus, the correct answer is:
**1,000**.
Since the repeating part "264" has 3 digits, you would multiply both sides of the equation by \( 1000 \) (not 10 or 100), as this will shift the decimal point three places to the right.
Thus, the correct answer is:
**1,000**.