If 102.7 is expressed in the form of p/q in lowest form, then q is :

To express a terminating decimal as a fraction p/q, write the decimal's digits over a power of 10 equal to the number of digits after the decimal point (one decimal place means the denominator is 10, two decimal places means 100, and so on), then reduce the fraction to its lowest form by dividing out any common factor shared by the numerator and the denominator.

1. 102.7 has exactly one digit after the decimal point, so write it as the fraction 1027/10.

2. Factorize the denominator: 10 = 2 x 5.

3. Check whether the numerator 1027 is divisible by 2: 1027 is an odd number, so it is not divisible by 2.

4. Check whether 1027 is divisible by 5: it does not end in 0 or 5, so it is not divisible by 5.

5. Since 1027 shares no common factor with 10, the fraction 1027/10 is already in its lowest form, so q = 10.

As an independent check, dividing 1027 by 10 gives back 102.7, confirming the fraction is correct; and since the greatest common factor of 1027 and 10 is 1, no further reduction is possible, so q = 10 is final.