Answer :
Sure! Let's convert the decimal 0.802 to both a fraction in simplest form and a percent.
### Converting 0.802 to a Fraction
1. Representation: We start by noting that 0.802 can be written as [tex]\(\frac{802}{1000}\)[/tex], since it has three decimal places.
2. Simplify the Fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (802) and the denominator (1000), and divide both by this GCD.
Let's find the GCD of 802 and 1000:
- Prime factorization of 802: [tex]\(802 = 2 \times 401\)[/tex]
- Prime factorization of 1000: [tex]\(1000 = 2^3 \times 5^3\)[/tex]
The only common factor is 2. Therefore, the GCD of 802 and 1000 is 2.
3. Divide by the GCD:
[tex]\[ \frac{802}{1000} = \frac{802 \div 2}{1000 \div 2} = \frac{401}{500} \][/tex]
Thus, the fraction in simplest form is [tex]\(\frac{401}{500}\)[/tex].
### Converting 0.802 to a Percent
1. Percent Representation: To convert a decimal to a percent, we multiply it by 100.
[tex]\[ 0.802 \times 100 = 80.2 \% \][/tex]
So, the decimal 0.802 is equivalent to:
- Fraction: [tex]\(\frac{401}{500}\)[/tex]
- Percent: [tex]\(80.2\%\)[/tex]
### Converting 0.802 to a Fraction
1. Representation: We start by noting that 0.802 can be written as [tex]\(\frac{802}{1000}\)[/tex], since it has three decimal places.
2. Simplify the Fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (802) and the denominator (1000), and divide both by this GCD.
Let's find the GCD of 802 and 1000:
- Prime factorization of 802: [tex]\(802 = 2 \times 401\)[/tex]
- Prime factorization of 1000: [tex]\(1000 = 2^3 \times 5^3\)[/tex]
The only common factor is 2. Therefore, the GCD of 802 and 1000 is 2.
3. Divide by the GCD:
[tex]\[ \frac{802}{1000} = \frac{802 \div 2}{1000 \div 2} = \frac{401}{500} \][/tex]
Thus, the fraction in simplest form is [tex]\(\frac{401}{500}\)[/tex].
### Converting 0.802 to a Percent
1. Percent Representation: To convert a decimal to a percent, we multiply it by 100.
[tex]\[ 0.802 \times 100 = 80.2 \% \][/tex]
So, the decimal 0.802 is equivalent to:
- Fraction: [tex]\(\frac{401}{500}\)[/tex]
- Percent: [tex]\(80.2\%\)[/tex]
