Question

Change the decimal to a fraction: 0.1213(1 point)
Responses

1213/10,000
the fraction with numerator 1213 and denominator 10 comma 000

This decimal is Irrational and cannot be written as a fraction
This decimal is Irrational and cannot be written as a fraction

1213/999

1 213/1,000

12 13/10

Change the decimal to a fraction: 0.123123123….(1 point)
Responses

123/999
123 over 999

12 13/10

This decimal is Irrational and cannot be written as a fraction
This decimal is Irrational and cannot be written as a fraction

123/1000
123 over 1000

1 23 100

Answer 1

To convert the decimals to fractions:

1. For the decimal **0.1213**:

This decimal can be expressed as a fraction by noting that it has four decimal places. Therefore, we can convert it as follows:

\[
0.1213 = \frac{1213}{10000}
\]

So the correct response is:
**1213/10,000**

2. For the repeating decimal **0.123123123...**:

This can be expressed as:
Let \( x = 0.123123123...\)

To eliminate the repeating part, we can multiply by 1000 (since there are three digits in the repeating cycle):
\[
1000x = 123.123123123...
\]
Then, we can subtract the original \( x \):
\[
1000x - x = 123.123123123... - 0.123123123...
\]
This simplifies to:
\[
999x = 123
\]
Now, solving for \( x \):
\[
x = \frac{123}{999}
\]

So the correct response is:
**123/999**

Thus, the correct answers are:
- For 0.1213: **1213/10,000**
- For 0.123123123...: **123/999**