Question

Записать периодическую дробь в виде обыкновенной: 3,2(3)​очень срочно... помогите!! Пожалуйста!!!!

Answer 1

Правильный ответ: 3 целых 7/30.
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Answer 2

Converting a Periodic Fraction to a Common Fraction

To convert a periodic fraction to a common fraction, we need to understand the given periodic fraction. In this case, the given periodic fraction is 3,2(3).

A periodic fraction consists of a non-repeating part and a repeating part enclosed in parentheses. In this case, the non-repeating part is 3, and the repeating part is 2(3).

To convert this periodic fraction to a common fraction, we can follow these steps:

Step 1: Identify the numerator and denominator of the non-repeating part. - In this case, the non-repeating part is 3, so the numerator is 3.

Step 2: Identify the numerator and denominator of the repeating part. - In this case, the repeating part is 2(3), where 3 repeats infinitely. To determine the numerator and denominator of the repeating part, we need to consider the number of digits in the repeating part. - Since the repeating part has one digit (3), the numerator of the repeating part is 3, and the denominator is 9 (since there is one digit, and each digit represents a power of 10).

Step 3: Combine the non-repeating and repeating parts. - To combine the non-repeating and repeating parts, we need to multiply the non-repeating part by the denominator of the repeating part and add the repeating part. - In this case, the non-repeating part is 3, and the repeating part is 2(3). The denominator of the repeating part is 9. - Multiplying the non-repeating part (3) by the denominator of the repeating part (9) gives us 27. - Adding the repeating part (2(3)) gives us 2(3) + 27.

Step 4: Simplify the combined fraction. - To simplify the combined fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. - In this case, the numerator is 2(3) + 27, and the denominator is 9. - The GCD of 2(3) + 27 and 9 is 3. - Dividing both the numerator and denominator by 3 gives us the simplified fraction.

Therefore, the periodic fraction 3,2(3) can be written as a common fraction.