Let's analyze the question step by step to determine which fraction is equal to the decimal number [tex]\(0.15\)[/tex].
### Step 1: Understanding the Decimal
First, let's convert the decimal [tex]\(0.15\)[/tex] to a fraction. To do this, recognize that:
[tex]\[ 0.15 = \frac{15}{100} \][/tex]
### Step 2: Simplifying the Fraction
Next, simplify the fraction [tex]\(\frac{15}{100}\)[/tex] by finding the greatest common divisor (GCD) of 15 and 100.
15 and 100 can both be divided by 5:
[tex]\[
\frac{15 \div 5}{100 \div 5} = \frac{3}{20}
\][/tex]
So, [tex]\(0.15\)[/tex] in its simplest fraction form is [tex]\(\frac{3}{20}\)[/tex].
### Step 3: Comparing with Given Choices
Now, we will compare this simplified fraction with the choices provided to find the correct match:
- Choice A. [tex]\(\frac{15}{10}\)[/tex] simplifies to [tex]\(\frac{3}{2}\)[/tex], which is not equal to [tex]\(\frac{3}{20}\)[/tex].
- Choice 8. [tex]\(\frac{3}{20}\)[/tex] is exactly what we calculated.
- Choice B. [tex]\(\frac{5}{20}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex], which is not equal to [tex]\(\frac{3}{20}\)[/tex].
- Choice D. [tex]\(\frac{100}{15}\)[/tex] simplifies to [tex]\(\frac{20}{3}\)[/tex], which is not equal to [tex]\(\frac{3}{20}\)[/tex].
### Conclusion
The correct fraction representation of [tex]\(0.15\)[/tex] is [tex]\(\frac{3}{20}\)[/tex], which corresponds to:
8. [tex]\(\frac{3}{20}\)[/tex]
