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Express the following decimals as fractions in their simplest form:

a) 0.58

b) [tex]0.065[/tex]

Sagot :

GinnyAnsweridn
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].
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