Decimal to Fraction Conversion To convert a terminating decimal to a fraction, follow these steps: Write the decimal as a fraction with 1 as the denominator. Multiply the numerator and denominator by a power of 10 that makes the numerator an integer. The power of 10 is determined by the number of decimal places. Simplify the resulting fraction to its lowest terms. Example: Convert $0.8965$ to a fraction Write the decimal as a fraction over 1: $$ \frac{0.8965}{1} $$ The decimal $0.8965$ has four decimal places. So, multiply the numerator and denominator by $10^4 = 10000$: $$ \frac{0.8965 \times 10000}{1 \times 10000} = \frac{8965}{10000} $$ Simplify the fraction. Find the greatest common divisor (GCD) of $8965$ and $10000$. Both numbers are divisible by 5. $8965 \div 5 = 1793$ $10000 \div 5 = 2000$ So the fraction becomes: $$ \frac{1793}{2000} $$ Check if $1793$ and $2000$ have any common factors other than 1. Prime factorization of $1793$: $1793$ is a prime number. Prime factorization of $2000$: $2^4 \times 5^3$ Since $1793$ is not 2 or 5, and it's a prime itself, there are no common factors. Therefore, $0.8965$ as a fraction in simplest form is $\frac{1793}{2000}$. General Steps For a decimal $D$ with $n$ decimal places: $$ D = \frac{\text{integer part of } (D \times 10^n)}{10^n} $$ Then simplify the fraction. Common Decimal-Fraction Equivalents Decimal Fraction $0.5$ $\frac{1}{2}$ $0.25$ $\frac{1}{4}$ $0.75$ $\frac{3}{4}$ $0.2$ $\frac{1}{5}$ $0.1$ $\frac{1}{10}$ $0.333...$ $\frac{1}{3}$ $0.125$ $\frac{1}{8}$
