Answer :
To convert the decimal 0.82 into a fraction in its simplest form, follow these steps:
1. Write the decimal as a fraction:
The decimal 0.82 can be expressed as [tex]\(\frac{82}{100}\)[/tex] because 82 is in the hundredths place.
2. Simplify the fraction:
- Find the greatest common divisor (GCD) of the numerator (82) and the denominator (100).
- The GCD of 82 and 100 is 2.
- Divide both the numerator and denominator by their GCD:
[tex]\[
\frac{82 \div 2}{100 \div 2} = \frac{41}{50}
\][/tex]
3. Verify it is in simplest form:
The fraction [tex]\(\frac{41}{50}\)[/tex] is already in its simplest form because 41 is a prime number and doesn't share any divisors with 50 other than 1.
Therefore, 0.82 can be written as [tex]\(\frac{41}{50}\)[/tex] in its simplest form.
1. Write the decimal as a fraction:
The decimal 0.82 can be expressed as [tex]\(\frac{82}{100}\)[/tex] because 82 is in the hundredths place.
2. Simplify the fraction:
- Find the greatest common divisor (GCD) of the numerator (82) and the denominator (100).
- The GCD of 82 and 100 is 2.
- Divide both the numerator and denominator by their GCD:
[tex]\[
\frac{82 \div 2}{100 \div 2} = \frac{41}{50}
\][/tex]
3. Verify it is in simplest form:
The fraction [tex]\(\frac{41}{50}\)[/tex] is already in its simplest form because 41 is a prime number and doesn't share any divisors with 50 other than 1.
Therefore, 0.82 can be written as [tex]\(\frac{41}{50}\)[/tex] in its simplest form.