What is the decimal equivalent of 8/3?
A. 2.6
B. 0.375
C. 2.67
D. 8.3
The Correct answer and Explanation is:
To find the decimal equivalent of the fraction 83\frac{8}{3}38, you can perform long division or use a calculator. Let’s explore both methods.
Long Division Method:
- Setup: Divide 8 by 3. Since 3 goes into 8 two times (as 3×2=63 \times 2 = 63×2=6), we write down 2.
- Subtraction: Subtract 666 from 888, which gives us 222 (i.e., 8−6=28 – 6 = 28−6=2).
- Bring Down a Zero: Next, add a decimal point and a zero to the 2, making it 20.
- Divide Again: Now, divide 20 by 3. The number 3 goes into 20 six times (as 3×6=183 \times 6 = 183×6=18). So, we write down 6.
- Subtract Again: Subtract 181818 from 202020, which gives us 222 (i.e., 20−18=220 – 18 = 220−18=2).
- Repeat the Process: You will notice that bringing down another zero gives you 20 again, and this process will repeat indefinitely.
This process shows that 83=2.666… \frac{8}{3} = 2.666…38=2.666…, which can be rounded to 2.672.672.67 for simplicity.
Using a Calculator: Alternatively, using a calculator to compute 8÷38 \div 38÷3 will yield approximately 2.666666… 2.666666…2.666666…, which is conventionally rounded to 2.672.672.67.
Conclusion: Among the options given:
- A. 2.6
- B. 0.375
- C. 2.67
- D. 8.3
The correct answer is C. 2.67.
This calculation is crucial in various mathematical contexts, including ratios, proportions, and conversions, helping to better understand the relationships between numbers. It also illustrates how fractions can represent non-terminating decimals, demonstrating the richness of the number system beyond whole numbers. Understanding decimal equivalents is essential in fields such as finance, science, and engineering, where precision in measurements and calculations is critical.