Write the repeating decimal as a fraction..600300300…

To write the repeating decimal as a fraction, we can follow these steps:

Step 1: Let's assign a variable to the repeating decimal. In this case, let's call it x. So, x = 0.600300300...

Step 2: Multiply both sides of the equation by a power of 10 that will shift the decimal point to the right of the repeating part. Since there are three digits in the repeating part, we can multiply by 1000. This gives us 1000x = 600.300300...

Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part. This gives us:

1000x - x = 600.300300... - 0.600300300... 999x = 600

Step 4: Solve for x by dividing both sides of the equation by 999:

x = 600 / 999

Step 5: Simplify the fraction if possible. In this case, we can divide both the numerator and denominator by their greatest common divisor, which is 3:

x = 200 / 333

So, the repeating decimal 0.600300300... can be written as the fraction 200/333.