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

Question

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