is 4/7 a repeating decimal
Yes, when 4 is divided by 7, the decimal representation is 0.5714285714285714..., which shows a repeating pattern of 5714.
To determine if a fraction is a repeating decimal, you need to convert it into decimal form and check if there is a repeating pattern.
To convert the fraction 4/7 into a decimal, divide the numerator (4) by the denominator (7):
4 ÷ 7 = 0.57142857...
As you can see, after the decimal point, the decimal digits 571428 repeat in the same order. Therefore, 4/7 is a repeating decimal.
To determine if a decimal representation is repeating or terminating, you can follow these steps for the fraction 4/7:
1. Divide the numerator (4) by the denominator (7): 4 ÷ 7.
- The quotient is 0.5714285714...
2. Check if the quotient has a pattern that repeats.
- Notice that the digits 571428 repeat indefinitely.
Therefore, 4/7 is a repeating decimal, where the repeating part is 571428.