Question

Convert 0, point, 5, 9, 50.595 to a fraction in simplest form and a percent.

Answer 1

To convert the decimal \(0.595\) to a fraction in simplest form, we can follow these steps:

1. Write the decimal as a fraction:
\[
0.595 = \frac{595}{1000}
\]

2. 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 \(5\).

3. 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: \(59.5\%\)