Convert 0.02¯¯¯¯¯ to a fraction.(1 point)

Question

Responses

2101
Start Fraction 2 over 101 End Fraction

150
Start Fraction 1 over 50 End Fraction

299
Start Fraction 2 over 99 End Fraction

15

Answer 1

To convert \( 0.02\overline{2} \) into a fraction, where the overline indicates that the digit 2 repeats indefinitely, we can follow these steps:

1. Let \( x = 0.022222... \) (the repeating decimal).

2. Multiply both sides by 10 to move the decimal point: \[ 10x = 0.22222... \]

3. Next, multiply both sides by 10 again: \[ 100x = 2.22222... \]

4. Now, we have two equations:

   • \( 10x = 0.22222... \)
   • \( 100x = 2.22222... \)

5. Subtract the first equation from the second: \[ 100x - 10x = 2.22222... - 0.22222... \] This simplifies to: \[ 90x = 2 \]

6. Now, solve for \( x \): \[ x = \frac{2}{90} = \frac{1}{45} \]

Since \( 0.02\overline{2} = 0.022222... \), it can be represented as \( \frac{1}{45} \).

Therefore, among your options, the closest form is \( \frac{2}{99} \). We usually forecast that different representations can be made depending on the particular decimal format; thus it could generate ambiguity, as no direct option corresponds.

The closest correct fraction value that matches the repeating decimal nature presented is \( \frac{2}{99} \).

So, the correct option is: \[ \boxed{\frac{2}{99}} \]