What is the decimal equivalent of 8/3
The Correct Answer and Explanation is:
The decimal equivalent of the fraction ( \frac{8}{3} ) is 2.6667 (rounded to four decimal places).
Explanation:
To convert a fraction like ( \frac{8}{3} ) to its decimal equivalent, we divide the numerator (8) by the denominator (3). This can be done using long division or a calculator.
Step 1: Set up the division problem.
We are dividing 8 by 3:
[
8 \div 3
]
Step 2: Perform the division.
When you divide 8 by 3, 3 goes into 8 two times because ( 3 \times 2 = 6 ). Subtract 6 from 8 to get a remainder of 2. Now, drop down a zero to continue the division.
[
8 – 6 = 2
]
Next, divide 20 by 3. 3 goes into 20 six times because ( 3 \times 6 = 18 ). Subtract 18 from 20 to get a remainder of 2 again.
[
20 – 18 = 2
]
This gives you another 6 in the decimal place. Since the remainder repeats the same pattern, we know that the decimal will continue indefinitely with 6’s. Hence, ( \frac{8}{3} ) is a repeating decimal.
The result is:
[
2.6666666\ldots
]
Step 3: Round the decimal.
In many practical applications, we round repeating decimals for simplicity. In this case, ( 2.6666666\ldots ) can be rounded to ( 2.6667 ) when we need a value with four decimal places.
Step 4: Final Answer
The decimal equivalent of ( \frac{8}{3} ) is ( 2.6667 ).
This type of repeating decimal occurs because 3 does not divide evenly into 8, leading to a recurring cycle of 6 in the quotient.