Question
To convert 0.264(repeating bar over 264)
to a rational number, you would set x
equal to 0.264(repeating bar over 264)
and then multiply both sides of the equation by what number?(1 point)
Responses
10
10
1,000
1,000
100
100
999
to a rational number, you would set x
equal to 0.264(repeating bar over 264)
and then multiply both sides of the equation by what number?(1 point)
Responses
10
10
1,000
1,000
100
100
999
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 has three digits (264), you would multiply both sides of the equation by 1,000 to shift the decimal point three places to the right:
\( 1,000x = 264.264264\ldots \)
Therefore, the correct response is:
**1,000**
\( x = 0.264264264\ldots \)
Since the repeating part has three digits (264), you would multiply both sides of the equation by 1,000 to shift the decimal point three places to the right:
\( 1,000x = 264.264264\ldots \)
Therefore, the correct response is:
**1,000**