To express the decimal 0.315 as a fraction in its lowest term, follow these steps:
1. Write the decimal as a fraction: The decimal 0.315 can be written as a fraction with 315 as the numerator and 1000 as the denominator since 0.315 means 315 thousandths.
[tex]\[
0.315 = \frac{315}{1000}
\][/tex]
2. Simplify the fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by that number. The GCD of 315 and 1000 is 5.
3. Divide the numerator and denominator by the GCD:
[tex]\[
\frac{315 \div 5}{1000 \div 5} = \frac{63}{200}
\][/tex]
4. Check if the fraction is in its simplest form: After the division, the fraction [tex]\(\frac{63}{200}\)[/tex] cannot be simplified further because 63 and 200 have no common factors other than 1.
Therefore, the fraction representation of 0.315 in its lowest term is [tex]\(\frac{63}{200}\)[/tex]. Thus, the correct answer is:
B. [tex]$\frac{63}{200}$[/tex]
