To convert the decimal \(0.595\) to a fraction in simplest form, we can follow these steps:
-
Write the decimal as a fraction: \[ 0.595 = \frac{595}{1000} \]
-
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator (595) and the denominator (1000).
-
The prime factorization of 595 is: \[ 595 = 5 \times 119, \quad \text{and} \quad 119 = 7 \times 17 \quad \Rightarrow \quad 595 = 5 \times 7 \times 17 \]
-
The prime factorization of 1000 is: \[ 1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3 \]
-
The common factor between 595 and 1000 is \(5\).
-
-
Divide the numerator and denominator by their GCD: \[ \frac{595 \div 5}{1000 \div 5} = \frac{119}{200} \]
Thus, the decimal \(0.595\) can be expressed as the fraction \(\frac{119}{200}\) in simplest form.
Next, to convert \(0.595\) to a percent, we multiply it by \(100\): \[ 0.595 \times 100 = 59.5% \]
In summary:
- Decimal \(0.595\) as a fraction in simplest form: \(\frac{119}{200}\)
- Decimal \(0.595\) as a percent: \(59.5%\)
1 answer