To convert each of the given decimals into the form \(\frac{p}{q}\), we follow these steps:
### (i) \(0.57\)
Step 1: Identify the decimal.
[tex]\[ 0.57 \][/tex]
Step 2: Write it as a fraction of the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers.
[tex]\[ 0.57 = \frac{57}{100} \][/tex]
Step 3: Simplify the fraction if necessary. In this case:
[tex]\[ \frac{57}{100} \][/tex]
The fraction is already in its simplest form.
Result:
[tex]\[ 0.57 = \frac{5134103575202365}{9007199254740992} \][/tex]
### (ii) \(0.176\)
Step 1: Identify the decimal.
[tex]\[ 0.176 \][/tex]
Step 2: Write it as a fraction of the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers.
[tex]\[ 0.176 = \frac{176}{1000} \][/tex]
Step 3: Simplify the fraction if necessary. In this case:
[tex]\[ \frac{176}{1000} \][/tex]
The fraction is already in its simplest form.
Result:
[tex]\[ 0.176 = \frac{3170534137668829}{18014398509481984} \][/tex]
### (iii) \(1.00001\)
Step 1: Identify the decimal.
[tex]\[ 1.00001 \][/tex]
Step 2: Write it as a fraction of the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers.
[tex]\[ 1.00001 = \frac{100001}{100000} \][/tex]
Step 3: Simplify the fraction if necessary. In this case:
[tex]\[ \frac{100001}{100000} \][/tex]
The fraction is already in its simplest form.
Result:
[tex]\[ 1.00001 = \frac{2251822331683385}{2251799813685248} \][/tex]
### (iv) \(25.125\)
Step 1: Identify the decimal.
[tex]\[ 25.125 \][/tex]
Step 2: Write it as a fraction of the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers.
[tex]\[ 25.125 = 25 + 0.125 = 25 + \frac{125}{1000} = 25 + \frac{1}{8} = \frac{25 \cdot 8}{8} + \frac{1}{8} = \frac{200}{8} + \frac{1}{8} = \frac{201}{8} \][/tex]
Result:
[tex]\[ 25.125 = \frac{201}{8} \][/tex]
These fractions represent the given decimals in the [tex]\(\frac{p}{q}\)[/tex] form.
