4.40 divided by 460. Since 460=10*46, we can simplify the problem by dividing 4.40 by 10 first. To do this we move the decimal point one place to the left: 0.440. We can also divide this result by 2 because 46=2*23. 0.440 divided by 2=0.220.
All that remains is to divide 0.220 by 23.
We use long division as if there were no decimal point.
23 won't divide into 2 or 22 so in the answer we need two zeroes after the dec pt. 23 divides into 220 9 times (9*23=207) leaving a remainder 13, which we combine with another zero to make 130.
9 is placed in the answer making 0.009. 23 goes into 130 5 times so 5 goes next to 9 in the answer.
And so on, calculating the remainder and bringing down zeroes indefinitely for as many dec places as necessary.
To 3 significant figures the answer is 0.00957, close to 0.01 which you quoted.