The decimal representation of $\frac{2}{3}$ is $0.6666 \ldots$, where the digit 6 repeats infinitely. To represent it correctly up to 4 digits, we consider only the first 4 decimal places:

$\frac{2}{3} \approx 0.6667$

Explanation:

• The fraction $\frac{2}{3} = 0.6666\ldots$.
• When rounding to 4 digits, we observe the 5th digit (which is 6 in this case). Since it is greater than or equal to 5, we round the 4th digit up.
• Thus, $0.6666 \ldots$ becomes $0.6667$ when rounded to 4 decimal places.

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Would you like a detailed explanation on floating-point representation in binary or decimal?

Related Questions:

1. How do you convert fractions to decimals step-by-step?
2. What are the rules for rounding off numbers in floating-point arithmetic?
3. How is a repeating decimal converted into its fractional representation?
4. What is the binary representation of $\frac{2}{3}$?
5. Why is floating-point precision important in numerical computations?

Tip:

When working with floating-point representations, always consider the rounding rules and the context where precision matters (e.g., engineering vs. financial applications).