Sure, let's express each of the given decimals as fractions in their simplest forms.
### Part (a) 0.58 as a fraction
1. Write the decimal as a fraction:
[tex]\[
0.58 = \frac{58}{100}
\][/tex]
2. Simplify the fraction:
- Find the Greatest Common Divisor (GCD) of the numerator and the denominator. Here, the GCD of 58 and 100 is 2.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{58 \div 2}{100 \div 2} = \frac{29}{50}
\][/tex]
So, [tex]\( 0.58 \)[/tex] as a simplified fraction is [tex]\( \frac{29}{50} \)[/tex].
### Part (b) 0.065 as a fraction
1. Write the decimal as a fraction:
[tex]\[
0.065 = \frac{65}{1000}
\][/tex]
2. Simplify the fraction:
- Find the Greatest Common Divisor (GCD) of the numerator and the denominator. Here, the GCD of 65 and 1000 is 5.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{65 \div 5}{1000 \div 5} = \frac{13}{200}
\][/tex]
So, [tex]\( 0.065 \)[/tex] as a simplified fraction is [tex]\( \frac{13}{200} \)[/tex].
### Final Answer
- [tex]\( 0.58 \)[/tex] as a fraction in simplest form is [tex]\( \frac{29}{50} \)[/tex].
- [tex]\( 0.065 \)[/tex] as a fraction in simplest form is [tex]\( \frac{13}{200} \)[/tex].
