Question

Объясниие ,как перевести в обычную дробь 0,(13)

Answer 1

Нужно писать как слышится например:0,13 то будет 13/100

Answer 2

Converting a Repeating Decimal to a Fraction

To convert a repeating decimal to a fraction, we can use a simple algebraic method. Let's take the repeating decimal 0,(13) as an example.

To begin, let's assign a variable to the repeating decimal. Let x = 0,(13).

Next, we multiply both sides of the equation by a power of 10 that eliminates the repeating part. Since there are two digits repeating, we multiply by 100:

100x = 13,(13)

Now, we subtract the original equation from the new equation to eliminate the repeating part:

100x - x = 13,(13) - 0,(13)

Simplifying the equation:

99x = 13

Finally, we solve for x by dividing both sides of the equation by 99:

x = 13/99

Therefore, the fraction equivalent of the repeating decimal 0,(13) is 13/99.

Conclusion

To convert the repeating decimal 0,(13) to a fraction, we followed the steps outlined above. The fraction equivalent is 13/99.