A carpenter has a piece of wood that is 2 m long and cuts it into 3 equal parts. He approximates the length of each part to 0.66 m. Calculate the absolute and percentage error.

The total length of the wood is $2 \text{ m}$, and it is cut into 3 equal parts.
True length of each piece $= \frac{2}{3} \text{ m}$.

The carpenter approximates the length of each piece to $0.66 \text{ m}$.

Absolute error is the absolute difference between the true value and the approximated value.
Absolute error $= \left| \frac{2}{3} - 0.66 \right|$
To perform the subtraction, convert 0.66 to a fraction: $0.66 = \frac{66}{100} = \frac{33}{50}$.
Absolute error $= \left| \frac{2}{3} - \frac{33}{50} \right|$
Find a common denominator, which is 150:
Absolute error $= \left| \frac{2 \times 50}{3 \times 50} - \frac{33 \times 3}{50 \times 3} \right|$
Absolute error $= \left| \frac{100}{150} - \frac{99}{150} \right|$
Absolute error $= \left| \frac{1}{150} \right| = \frac{1}{150} \text{ m}$.

The formula for percentage error is:
Percentage Error $= \frac{\text{Absolute Error}}{\text{True Value}} \times 100\%$
Percentage Error $= \frac{\frac{1}{150}}{\frac{2}{3}} \times 100\%$
Percentage Error $= \frac{1}{150} \times \frac{3}{2} \times 100\%$
Percentage Error $= \frac{3}{300} \times 100\%$
Percentage Error $= \frac{1}{100} \times 100\%$
Percentage Error $= 1\%$

The percentage error due to this approximation is $\boxed{1\%}$.