0.62 with the 2 repeating as a fraction

0.62 with the 2 repeating as a fraction

The correct answer and explanation is:

To express 0.620.62 with the repeating decimal 0.62‾0.\overline{62} (where 62 repeats indefinitely) as a fraction, follow these steps:

Step 1: Set up the equation

Let x=0.62‾x = 0.\overline{62}.

This means that the decimal portion repeats every two digits. To eliminate the repeating part, multiply both sides of the equation by 100, since the repeating block is two digits long: 100x=62.62‾100x = 62.\overline{62}

Step 2: Subtract the original equation from the new one

Now, subtract the original equation x=0.62‾x = 0.\overline{62} from 100x=62.62‾100x = 62.\overline{62}: 100x−x=62.62‾−0.62‾100x – x = 62.\overline{62} – 0.\overline{62}

This simplifies to: 99x=6299x = 62

Step 3: Solve for xx

Now, divide both sides of the equation by 99 to isolate xx: x=6299x = \frac{62}{99}

Thus, 0.62‾=62990.\overline{62} = \frac{62}{99}.

Step 4: Simplify the fraction

At this point, the fraction 6299\frac{62}{99} is in its simplest form. The greatest common divisor (GCD) of 62 and 99 is 1, so the fraction cannot be reduced further.

Final Answer

Therefore, the repeating decimal 0.62‾0.\overline{62} is equivalent to the fraction 6299\frac{62}{99}.

Explanation

The key idea is to set up an equation for the repeating decimal, then eliminate the repeating part by multiplying by a power of 10. By subtracting the original equation from the new one, the repeating part cancels out, leaving you with a simple linear equation to solve. Finally, simplifying the fraction, if possible, gives the final result. This method works for any repeating decimal, whether the repeating block has one digit, two digits, or more.