Question
Rational Numbers in Different Forms Practice
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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)
Answers
GPT-4o mini
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.**
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.**