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