In decimal notation, what is the value of the fraction 2/3 when it is expressed correct to two decimal places?

Introduction / Context:
Converting rational numbers (fractions) to decimal form is a basic but essential skill in quantitative aptitude. In this question, we are asked to convert the fraction 2/3 into a decimal and then match it with the closest choice given, expressed using two decimal places. This type of conversion is also frequently used in percentage calculations and comparisons in competitive exams.

Given Data / Assumptions:

• Given fraction: 2/3.
• We need its decimal representation.
• Options use two decimal places, so rounding or truncation must be considered.

Concept / Approach:
To convert a fraction to a decimal, divide the numerator by the denominator. Here, we need to compute 2 ÷ 3. The result will be a repeating decimal. Once we know the repeating decimal, we can round it to two decimal places to match one of the answer choices. Remember basic rules of rounding: if the third decimal place is 5 or more, we round the second place up by 1.

Step-by-Step Solution:
Step 1: Start with the fraction 2/3. Step 2: Perform the division 2 ÷ 3. Step 3: 3 goes into 2 zero times, so we write 0.x and proceed with 20 ÷ 3. Step 4: 3 goes into 20 six times (6 * 3 = 18) with remainder 2, giving 0.6. Step 5: The remainder 2 repeats, so the digits 6 continue: 2/3 = 0.6666..., a recurring decimal. Step 6: To express 0.6666... to two decimal places, we look at the third decimal digit: 0.666... has 6 as the third digit. Step 7: Because the third digit (6) is greater than or equal to 5, we round 0.66 up to 0.67.

Verification / Alternative Check:
We know that 1/3 = 0.3333..., and multiplying both sides by 2 gives 2/3 = 0.6666.... Again, rounding 0.6666... to two decimal places yields 0.67, so this confirms our result through a simple proportional argument.

Why Other Options Are Wrong:
0.47 is far smaller than 2/3 and does not approximate 0.6666....
6.77 is much larger than 1, whereas 2/3 is less than 1, so this option is absurd here.
0.07 is extremely small and clearly not equal to 2/3.
Only 0.67 is a correct two decimal place approximation to 2/3.

Common Pitfalls:
Learners sometimes confuse 2/3 with 0.63 or 0.6 due to careless rounding or truncation. Truncating 0.6666... to 0.66 instead of rounding it to 0.67 is a frequent error. Always use proper rounding rules and ensure you understand the difference between truncation and rounding.

Final Answer:
The decimal representation of 2/3 correct to two decimal places is 0.67.