To express each of the given decimal numbers as a fraction in the form [tex]\(\frac{p}{q}\)[/tex], follow these steps:
### Step-by-Step Solution
#### a. 0.45
1. The decimal number is 0.45.
2. To convert 0.45 to a fraction, we find that:
[tex]\[
0.45 = \frac{8106479329266893}{18014398509481984}
\][/tex]
3. This fraction cannot be simplified further.
So, [tex]\(0.45\)[/tex] is expressed as:
[tex]\[
0.45 = \frac{8106479329266893}{18014398509481984}
\][/tex]
#### b. 0.9
1. The decimal number is 0.9.
2. To convert 0.9 to a fraction, we find that:
[tex]\[
0.9 = \frac{8106479329266893}{9007199254740992}
\][/tex]
3. This fraction cannot be simplified further.
So, [tex]\(0.9\)[/tex] is expressed as:
[tex]\[
0.9 = \frac{8106479329266893}{9007199254740992}
\][/tex]
#### c. 0.148
1. The decimal number is 0.148.
2. To convert 0.148 to a fraction, we find that:
[tex]\[
0.148 = \frac{5332261958806667}{36028797018963968}
\][/tex]
3. This fraction cannot be simplified further.
So, [tex]\(0.148\)[/tex] is expressed as:
[tex]\[
0.148 = \frac{5332261958806667}{36028797018963968}
\][/tex]
#### d. 0.004
1. The decimal number is 0.004.
2. To convert 0.004 to a fraction, we find that:
[tex]\[
0.004 = \frac{1152921504606847}{288230376151711744}
\][/tex]
3. This fraction cannot be simplified further.
So, [tex]\(0.004\)[/tex] is expressed as:
[tex]\[
0.004 = \frac{1152921504606847}{288230376151711744}
\][/tex]
### Summary
The decimal numbers expressed as fractions are:
[tex]\[
\begin{aligned}
a. & \ 0.45 = \frac{8106479329266893}{18014398509481984} \\
b. & \ 0.9 = \frac{8106479329266893}{9007199254740992} \\
c. & \ 0.148 = \frac{5332261958806667}{36028797018963968} \\
d. & \ 0.004 = \frac{1152921504606847}{288230376151711744}
\end{aligned}
\][/tex]
