6 \cdot 10^5 is how many times as large as 3\cdot10^{3}

To find how many times (6 \cdot 10^5) is as large as (3 \cdot 10^3), we can set up the following division:

[ \frac{6 \cdot 10^5}{3 \cdot 10^3} ]

Now let's simplify this expression:

1. Divide the coefficients: [ \frac{6}{3} = 2 ]

2. Divide the powers of 10: [ \frac{10^5}{10^3} = 10^{5-3} = 10^2 ]

Now, combine the results from steps 1 and 2: [ 2 \cdot 10^2 ]

Finally, we can express (2 \cdot 10^2) as: [ 2 \cdot 100 = 200 ]

Thus, (6 \cdot 10^5) is (200) times as large as (3 \cdot 10^3).