1. **State the problem:** Simplify the decimal number 0.035 into a fraction in simplest form. 2. **Convert decimal to fraction:** The decimal 0.035 means 35 thousandths, so we write it as: $$\frac{35}{1000}$$ 3. **Simplify the fraction:** Find the greatest common divisor (GCD) of 35 and 1000. - Factors of 35: 1, 5, 7, 35 - Factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 - The greatest common factor is 5. 4. **Divide numerator and denominator by 5:** $$\frac{35 \div 5}{1000 \div 5} = \frac{7}{200}$$ 5. **Final answer:** The simplified fraction of 0.035 is: $$\frac{7}{200}$$