To express \(\(0.214\)\) as a fraction, we need to convert the decimal to a fraction and then simplify it.
1. Let \(\( x \)\) be the decimal number:
\(\[
x = 0.214
\]\)
2. Identify the number of digits in the decimal part.
Since 0.214 has three digits after the decimal point, we need to multiply \(\( x \)\) by \(\( 1000 \)\) to convert it to a whole number.
3. Multiply both sides of the equation by \(\( 1000 \)\):
\(\[
1000x = 214
\]\)
4. Express \(\( x \)\) as a fraction:
\(\[
x = \frac{214}{1000}
\]\)
5. Simplify the fraction:
To simplify \(\( \frac{214}{1000} \)\), we find the greatest common divisor (GCD) of 214 and 1000. The GCD of 214 and 1000 is 2.
\(\[
\frac{214}{1000} = \frac{214 \div 2}{1000 \div 2} = \frac{107}{500}
\]\)
6. Final simplified fraction:
Therefore, the decimal \(\( 0.214 \)\) expressed as a fraction is:
\(\[
\boxed{\frac{107}{500}}
\]\)
This gives us the final result that \(\( 0.214 \)\) as a simplified fraction is \(\( \frac{107}{500} \)\).
