4/7 as a Decimal
In mathematics, a decimal is a number that can be expressed as a fraction of two integers, where the denominator is a power of 10. For example, the number 0.5 is a decimal because it can be expressed as the fraction 1/2, which is equivalent to 0.500000…, where the zeros repeat infinitely.
The fraction 4/7 is a non-terminating, repeating decimal. This means that the decimal expansion of 4/7 never ends and has a repeating pattern. The repeating pattern in this case is 571.
To convert a fraction to a decimal, we can use long division. In this case, the long division process would be as follows:
7) 4.0000... 0. 4 28 0 28 0 0 0 The remainder of 4/7 is 4, which is the same as the original numerator. This indicates that the decimal expansion of 4/7 is repeating. The repeating pattern begins after the first decimal place, which is 5.
Therefore, 4/7 as a decimal is equal to 0.571428571428…, where the 571 repeats infinitely.
Related Questions
- Is 4/7 a terminating or non-terminating decimal?
4/7 is a non-terminating decimal because the decimal expansion of 4/7 never ends.
- What is the repeating pattern in the decimal expansion of 4/7?
The repeating pattern in the decimal expansion of 4/7 is 571.
- How can we convert a fraction to a decimal using long division?
To convert a fraction to a decimal using long division, we follow these steps:
- Divide the numerator by the denominator.
- If the remainder is not zero, bring down a zero and continue dividing.
- If the remainder is zero, the decimal expansion is terminating. If the remainder is not zero, the decimal expansion is repeating.
- Continue dividing until the remainder repeats.
The repeating pattern begins after the last digit that does not repeat.
