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

Answer 1

just tell me the answer

Answer 2

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.

Answer 3

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:

**\( \frac{7}{50} \)**.