What is decimal form of 4/7 and what is the decimal expansion

What is decimal form of 4/7 and what is the decimal expansion

The Correct Answer and Explanation is:

Correct Answer: The decimal form of 4/7 is a non-terminating, repeating decimal.

The decimal expansion is 

0.571428‾0.571428

This is equivalent to writing 0.571428571428… with the digits continuing in that pattern forever.

Explanation

The term “decimal expansion” refers to the process of representing a fraction as a number in the base-10 system using a decimal point. To convert any fraction into its decimal form, you divide the numerator (the top number) by the denominator (the bottom number). For the fraction 4/7, we perform the division 4 ÷ 7.

Here is the step-by-step long division process:

1. Since 7 cannot go into 4, we place a decimal point and add a zero, making it 4.0.
2. 40 ÷ 7 = 5 with a remainder of 5. (Our decimal is now 0.5…)
3. We bring down another zero, making it 50.
4. 50 ÷ 7 = 7 with a remainder of 1. (Our decimal is now 0.57…)
5. We bring down another zero, making it 10.
6. 10 ÷ 7 = 1 with a remainder of 3. (Our decimal is now 0.571…)
7. We bring down another zero, making it 30.
8. 30 ÷ 7 = 4 with a remainder of 2. (Our decimal is now 0.5714…)
9. We bring down another zero, making it 20.
10. 20 ÷ 7 = 2 with a remainder of 6. (Our decimal is now 0.57142…)
11. We bring down another zero, making it 60.
12. 60 ÷ 7 = 8 with a remainder of 4. (Our decimal is now 0.571428…)

At this stage, our remainder is 4, which is the same number we started with. This means the entire sequence of remainders will now repeat, and therefore the sequence of digits in our answer (571428) will also repeat infinitely. This creates a non-terminating, repeating decimal. To show this repetition concisely, we place a bar (called a vinculum) over the repeating block of digits, giving us the final, precise answer: 

0.571428‾0.571428

.