4 2/3 as a Repeating Decimal
When we convert a mixed number like 4 2/3 to a decimal, we get a repeating decimal. But what does this mean, and how can we write it exactly?
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In other words, it's a decimal that has a pattern of digits that goes on forever. For example, the decimal 0.12341234... is a repeating decimal because the sequence "1234" repeats over and over again.
Converting 4 2/3 to a Decimal
To convert 4 2/3 to a decimal, we need to divide the numerator (2) by the denominator (3). This gives us:
2 ÷ 3 = 0.666...
As you can see, the decimal 0.666... is a repeating decimal because the digit 6 repeats indefinitely.
Writing 4 2/3 as a Repeating Decimal
So, how can we write 4 2/3 exactly as a repeating decimal? One way to do this is to write the whole number part (4) separately from the repeating decimal part. We can do this as follows:
4 2/3 = 4 + 0.666... = 4.(6)
The dot above the 6 indicates that the digit 6 repeats indefinitely.
Conclusion
In conclusion, 4 2/3 can be converted to a repeating decimal by dividing the numerator by the denominator. The resulting decimal is 0.666..., which can be written exactly as 4.(6) with the dot above the 6 indicating that the digit 6 repeats indefinitely. Repeating decimals are a fundamental concept in mathematics, and understanding them is essential for working with fractions and decimals.
