What is the decimal equivalent of 8/3
The Correct Answer and Explanation is:
The decimal equivalent of ( \frac{8}{3} ) is approximately 2.6667 (when rounded to four decimal places).
Explanation:
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). Here, you have ( \frac{8}{3} ), so you need to perform the division ( 8 \div 3 ).
- Set up the Division: Place 8 as the dividend (inside the division symbol) and 3 as the divisor (outside the division symbol).
- Divide:
- First, see how many times 3 can go into 8. It goes 2 times, since ( 3 \times 2 = 6 ), which is less than 8.
- Subtract 6 from 8, leaving a remainder of 2.
- Add Decimal: Since there’s a remainder, add a decimal point to the quotient (the answer) and add a zero to the remainder, making it 20.
- Continue Dividing:
- Now, divide 20 by 3. It goes 6 times (since ( 3 \times 6 = 18 )).
- Subtract 18 from 20, leaving a remainder of 2 again.
- Add another zero to make it 20 again, and repeat the process.
This repeating pattern results in the decimal 2.666…, which is a recurring decimal often represented as 2.6667 when rounded to four decimal places, or 2.\overline{6} to indicate the repeating digit.
Understanding Recurring Decimals:
In this case, 2.666… is an example of a repeating or recurring decimal because the digit 6 repeats indefinitely. This happens because 3 does not divide evenly into 8, and as you continue the division, you get the same remainder, causing the decimal part to repeat.
Practical Application:
Knowing how to convert fractions like ( \frac{8}{3} ) to decimals is useful in math, science, finance, and everyday calculations, as decimals are often easier to work with in various applications than fractions.