How many of the following statements are true?

I) $$(260)_7+\left(740\right)_8=\left(514\right)_{11}$$

II)$$\left(824\right)_9+\left(101101\right)_2=\left(710\right)_{10}$$

III) $$\left(0.353\right)_6=\left(0.505\right)_{10}$$

IV) $$\left(0.11111\right)_2=\left(0.96875\right)_{10}$$

I) $$(260)_7+\left(740\right)_8=\left(514\right)_{11}$$

$$(260)_7 = 2*7^2+6*7 = 140$$

$$\left(740\right)_8 = 7*8^2+4*8 = 480$$

140+480 =620

$$(620)_{10}=(514)_{11}$$

II)$$\left(824\right)_9+\left(101101\right)_2=\left(710\right)_{10}$$

$$\left(824\right)_9 = 8*9^2+2*9+4 = 670$$

$$(101101)_2=(1\times2^5)+(0\times2^4)+(1\times2^3)+(1\times2^2)+(0\times2^1)+(1\times2^0)\ =\ (45)_{10}$$

670+45 = $$(715)_{10}$$

III) $$\left(0.353\right)_6=\left(0.505\right)_{10}$$

$$3\cdot\frac{1}{6}+5\cdot\frac{1}{6\cdot6}+3\cdot\frac{1}{6\cdot6\cdot6}=\frac{1}{2}+\frac{5}{36}+\frac{1}{72}$$

This is clearly greater than 0.55. So, this is incorrect.

IV) $$\left(0.11111\right)_2=\left(0.96875\right)_{10}$$

$$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}=0.5+0.25+0.125+0.0625+0.03125=0.96875$$

So, this is a correct statement.

I and IV are the only correct statements.