Express Each of the Following Decimals in the Form p/q
Question: Express each of the following decimals in the form \( \frac{p}{q} \):
- (i) 0.39
- (ii) 0.750
- (iii) 2.15
Solution:
(i) Convert 0.39 into p/q form
\[ 0.39 = \frac{39}{100} \]
This is already in simplest form.
Answer: \( \frac{39}{100} \)
(ii) Convert 0.750 into p/q form
\[ 0.750 = \frac{750}{1000} \]
Simplify by dividing numerator and denominator by 250:
\[ \frac{750}{1000} = \frac{3}{4} \]
Answer: \( \frac{3}{4} \)
(iii) Convert 2.15 into p/q form
\[ 2.15 = \frac{215}{100} \]
Simplify by dividing by 5:
\[ \frac{215}{100} = \frac{43}{20} \]
Answer: \( \frac{43}{20} \)
Final Answers:
- \(0.39 = \frac{39}{100}\)
- \(0.750 = \frac{3}{4}\)
- \(2.15 = \frac{43}{20}\)
Concept Used:
To convert a decimal into a fraction, write it as a fraction with denominator as a power of 10 and simplify it. :contentReference[oaicite:0]{index=0}