Question
Convert 0.14¯¯¯¯¯ to a fraction.(1 point)
Responses
750
Start Fraction 7 over 50 End Fraction
14101
Start Fraction 14 over 101 End Fraction
7500
Start Fraction 7 over 500 End Fraction
1499
Responses
750
Start Fraction 7 over 50 End Fraction
14101
Start Fraction 14 over 101 End Fraction
7500
Start Fraction 7 over 500 End Fraction
1499
Answers
Answer
just tell me the answer
Answered by
GPT-4o mini
To convert the repeating decimal \( 0.14\overline{14} \) into a fraction, we can follow these steps:
Let \( x = 0.14\overline{14} \).
First, multiply \( x \) by 100 to shift the decimal point two places to the right:
\[
100x = 14.14\overline{14}
\]
Next, multiply \( x \) by 10000 to shift the decimal point four places to the right:
\[
10000x = 1414.14\overline{14}
\]
Now, subtract the first equation from the second:
\[
10000x - 100x = 1414.14\overline{14} - 14.14\overline{14}
\]
This simplifies to:
\[
9900x = 1400
\]
Now, solving for \( x \):
\[
x = \frac{1400}{9900}
\]
Next, we can simplify the fraction:
\[
\frac{1400 \div 100}{9900 \div 100} = \frac{14}{99}
\]
Thus, the repeating decimal \( 0.14\overline{14} \) as a fraction is \( \frac{14}{99} \).
Now based on your options regarding \( 0.14\overline{14} \):
1. \( \frac{7}{50} \)
2. \( \frac{14}{101} \)
3. \( \frac{7}{500} \)
4. \( \frac{14}{99} \)
None of the provided options match \( \frac{14}{99} \).
If you meant \( 0.14\) (which is not repeating), that would be a different case. Since we were processing \( 0.14\overline{14} \), the correct answer is not present in your responses. However, if it was \( 0.14\) alone, the answer would be \( \frac{14}{100} = \frac{7}{50}\).
Please clarify if you were asking about a different repeating decimal.
Let \( x = 0.14\overline{14} \).
First, multiply \( x \) by 100 to shift the decimal point two places to the right:
\[
100x = 14.14\overline{14}
\]
Next, multiply \( x \) by 10000 to shift the decimal point four places to the right:
\[
10000x = 1414.14\overline{14}
\]
Now, subtract the first equation from the second:
\[
10000x - 100x = 1414.14\overline{14} - 14.14\overline{14}
\]
This simplifies to:
\[
9900x = 1400
\]
Now, solving for \( x \):
\[
x = \frac{1400}{9900}
\]
Next, we can simplify the fraction:
\[
\frac{1400 \div 100}{9900 \div 100} = \frac{14}{99}
\]
Thus, the repeating decimal \( 0.14\overline{14} \) as a fraction is \( \frac{14}{99} \).
Now based on your options regarding \( 0.14\overline{14} \):
1. \( \frac{7}{50} \)
2. \( \frac{14}{101} \)
3. \( \frac{7}{500} \)
4. \( \frac{14}{99} \)
None of the provided options match \( \frac{14}{99} \).
If you meant \( 0.14\) (which is not repeating), that would be a different case. Since we were processing \( 0.14\overline{14} \), the correct answer is not present in your responses. However, if it was \( 0.14\) alone, the answer would be \( \frac{14}{100} = \frac{7}{50}\).
Please clarify if you were asking about a different repeating decimal.
Answered by
GPT-4o mini
The fraction representation of \( 0.14\overline{14} \) does not match any of the provided options. However, if you're looking for \( 0.14 \) (not repeating), the correct answer would be \( \frac{7}{50} \).
If you are specifically looking to represent \( 0.14\overline{14} \), the correct fraction is \( \frac{14}{99} \), which is not among the options you've listed.
If forced to choose from the options you provided, the answer that seems most appropriate for a non-repeating \( 0.14 \) would be:
**\( \frac{7}{50} \)**.
If you are specifically looking to represent \( 0.14\overline{14} \), the correct fraction is \( \frac{14}{99} \), which is not among the options you've listed.
If forced to choose from the options you provided, the answer that seems most appropriate for a non-repeating \( 0.14 \) would be:
**\( \frac{7}{50} \)**.
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