To express the terminating decimal number 0.205 as a quotient of two integers, follow these steps:
1. Write the decimal as a fraction:
[tex]\[
0.205 = \frac{205}{1000}
\][/tex]
2. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator (205) and the denominator (1000). We need to simplify this fraction to its lowest form.
3. Find the GCD of 205 and 1000. The GCD of 205 and 1000 is 5.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{205 \div 5}{1000 \div 5} = \frac{41}{200}
\][/tex]
Thus, the quotient in its lowest terms is:
[tex]\[
0.205 = \frac{41}{200}
\][/tex]
