To express the decimal number [tex]\( 0.6 \)[/tex] as a fraction [tex]\(\frac{p}{q}\)[/tex] where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers and [tex]\( q \neq 0 \)[/tex], follow these steps:
1. Understand the Problem:
We are given the decimal number [tex]\( 0.6 \)[/tex]. The goal is to write this number in the form of a fraction, [tex]\(\frac{p}{q}\)[/tex], where both [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers.
2. Convert the Decimal to a Fraction:
Start by recognizing that [tex]\( 0.6 \)[/tex] is a decimal number representing six-tenths. This can initially be written as:
[tex]\[
0.6 = \frac{6}{10}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\frac{6}{10}\)[/tex], find the greatest common divisor (GCD) of the numerator (6) and the denominator (10). The GCD of 6 and 10 is 2. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\][/tex]
4. Check the Result:
The fraction [tex]\(\frac{3}{5}\)[/tex] is in its simplest form because the numerator (3) and the denominator (5) have no common divisor other than 1.
Thus, the decimal number [tex]\( 0.6 \)[/tex] expressed as a fraction in its simplest form is:
[tex]\[
\frac{3}{5}
\][/tex]
In conclusion, [tex]\( 0.6 = \frac{p}{q} \)[/tex] where [tex]\( p = 3 \)[/tex] and [tex]\( q = 5 \)[/tex]. Therefore, the fraction representation is [tex]\(\frac{3}{5}\)[/tex].
