To express the number 13.523 in the form [tex]\(\frac{p}{q}\)[/tex], follow these detailed steps:
1. Identify the integer part and the decimal part of the number:
- The integer part of 13.523 is [tex]\(13\)[/tex].
- The decimal part of 13.523 is [tex]\(0.523\)[/tex].
2. Convert the decimal part into a fraction:
- To convert [tex]\(0.523\)[/tex] into a fraction, recognize that [tex]\(0.523\)[/tex] is the same as [tex]\(\frac{523}{1000}\)[/tex].
3. Simplify the fraction if necessary:
- The fraction [tex]\(\frac{523}{1000}\)[/tex] can be simplified if the numerator and the denominator have any common factors. In this case, [tex]\(523\)[/tex] is a prime number, and thus the fraction [tex]\(\frac{523}{1000}\)[/tex] is already in its simplest form.
4. Combine the integer part with the fraction:
- Express [tex]\(13.523\)[/tex] as the sum of its integer part and its decimal part as a fraction: [tex]\(13 + \frac{523}{1000}\)[/tex].
5. Convert the mixed number to an improper fraction:
- To convert [tex]\(13 + \frac{523}{1000}\)[/tex] to an improper fraction, use the following formula:
[tex]\[
\text{Improper fraction} = \left( \text{Integer part} \times \text{Denominator of the fraction} \right) + \text{Numerator of the fraction}
\][/tex]
- Plugging in the values, we have:
[tex]\[
13 + \frac{523}{1000} = \frac{(13 \times 1000) + 523}{1000} = \frac{13000 + 523}{1000} = \frac{13523}{1000}
\][/tex]
6. Final result:
- Therefore, [tex]\(13.523\)[/tex] can be expressed in the form [tex]\(\frac{p}{q}\)[/tex] as:
[tex]\[
\frac{13523}{1000}
\][/tex]
In summary, the number 13.523 can be written as the fraction [tex]\(\frac{13523}{1000}\)[/tex].
