Question

Помогите!! Перетворити 14 2/5 y періодичний десятковий дріб і знайти його десятковенаближення до тисячних.

Answer 1

Ответ:

Пошаговое объяснение:

14 2/5=14,400

Answer 2

Converting 14 2/5 to a Periodic Decimal and Finding its Decimal Approximation to the Thousandths

To convert 14 2/5 to a periodic decimal and find its decimal approximation to the thousandths, we can follow these steps:

1. Convert the mixed number 14 2/5 to an improper fraction. 2. Perform the division to convert the improper fraction to a decimal. 3. Identify the repeating pattern in the decimal to express it as a periodic decimal. 4. Round the periodic decimal to the thousandths place for the decimal approximation.

Step 1: Convert the Mixed Number to an Improper Fraction

The mixed number 14 2/5 can be converted to an improper fraction by multiplying the whole number (14) by the denominator (5) and adding the numerator (2). This gives us:

14 2/5 = (14 * 5 + 2)/5 = 72/5

Step 2: Perform the Division to Convert the Improper Fraction to a Decimal

Performing the division 72 ÷ 5 gives us a decimal value:

72 ÷ 5 = 14.4

Step 3: Identify the Repeating Pattern in the Decimal

The decimal value 14.4 does not have a repeating pattern, so we need to express it as a periodic decimal. To do this, we can represent 14.4 as 14.4000... where the pattern of 4000 repeats infinitely.

Step 4: Find the Decimal Approximation to the Thousandths

Rounding 14.4000... to the thousandths place gives us the decimal approximation:

14.400

Therefore, the decimal approximation of the periodic decimal 14 2/5 is 14.400 to the thousandths.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.