3.3.4 In the form: .abcbcbc …

Again, you can repeat the process above for variances. In this example we can represent $.abcbc \dots$ can be represented in fraction form:

$$.abcbcbc \dots = \frac{abc - a}{990}$$

Where the $abc$ represents the three-digit number $abc$ (not the product $a \cdot b \cdot c$). Here is an example:

$$.437373737 \dots = \frac{437 - 4}{990} = \frac{433}{990}$$

It is important for the Number Sense test to reduce all fractions. This can sometimes be the tricky part. The easiest way to check for reducibility is to see if you can divide the numerator by 2, 3, or 5. In the above example, 433 is not divisible by 2, 3, 5 so the fraction is in its lowest form.

Here is an example where you can reduce the fraction:

$$.2474747 \dots = \frac{247 - 2}{990} = \frac{245}{990} = \frac{49}{198}$$

Problem Set 3.3.4