To express the numbers 0.6, 0.7, and 0.47 in p/q form with a bar on the 7, we need to convert these numbers into fractions. Let's break down the process step-by-step.

Converting 0.6 into a fraction:
To convert 0.6 into a fraction, we can write it as 6/10. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 2.
So, 6/10 simplifies to 3/5.

Converting 0.7 into a fraction:
To convert 0.7 into a fraction, we can write it as 7/10. This fraction is already in its simplest form.

Converting 0.47 into a fraction:
To convert 0.47 into a fraction, we need to determine its place value. 0.47 has two decimal places, so we can write it as 47/100. This fraction can also be simplified by dividing both the numerator and denominator by their GCD, which is 1 in this case.
So, 47/100 is already in its simplest form.

Expressing the fractions in p/q form with a bar on the 7:
To express fractions with a recurring decimal in p/q form, we need to identify the recurring part of the decimal. In this case, the recurring part is 7.

Converting 3/5 to p/q form:
To express 3/5 in p/q form with a bar on the 7, we can write it as 0.6̅.
The bar on the 7 indicates that the digit 7 repeats infinitely.

Converting 7/10 to p/q form:
To express 7/10 in p/q form with a bar on the 7, we can write it as 0.7̅.
Again, the bar on the 7 indicates that the digit 7 repeats infinitely.

Converting 47/100 to p/q form:
To express 47/100 in p/q form with a bar on the 7, we can write it as 0.47̅.
The bar on the 7 indicates that the digit 7 repeats infinitely.

In summary, the p/q forms of 0.6, 0.7, and 0.47 with a bar on the 7 are:
- 0.6̅ = 3/5
- 0.7̅ = 7/10
- 0.47̅ = 47/100

These fractions represent the given decimal numbers in their simplest form with the recurring digit 7 indicated by a bar.