The simplest fraction for is . Write the upper bound as a fraction with the same denominator:
.
Hence the range for would be:
.
If the denominator of is also , then the range for its numerator (call it ) would be . Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than .
To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)
.
.
At this point, the difference between the numerators is now . That allows a number ( in this case) to fit between the bounds. However, can't be written as finite decimals.
Try multiplying the numerator and the denominator by a different number.
.
.
.
.
.
.
It is important to note that some expressions for can be simplified. For example, because of the common factor .