0.303030303 to the nearest hundreth

Question

The motion of a pendulum can be modeled by 2=(all under one square root) l over 3.3 where t is time and l is length of the pendulum in feet. If the pendulum takes 2 seconds to complete one swing , how long is the pendulum? Round to the nearest hundreth.

Answer 1

round2(0.303030303030...)=0.30

Answer 2

T=2(pi)sqrt(l/g), so 2=2(pi)sqrt(l/9.81); l/9.81=1/(pi)^2; l=9.81/(pi)^2=0.99396=99cm to the nearest cm (hundredth of a metre)=3.26 ft (1m=3.28 ft). Using the formula T=2sqrt(l/3.3), when T=2, sqrt(l/3.3)=1 so l=3.30 ft. (3.26 ft compares well with 3.30 ft to the nearest hundredth of a foot). T=2sqrt(l/3.3) is an approximation of 2sqrt(l/(9.81*3.28/(pi)^2))

Answer 3

.30, which could be simplified to .3. It looks like the nearest tenth, but really, it's in hundredths.