Question

write each decimal as a fraction or mixed number in simplest form. \\(1.\\ 0.6 = \frac{3}{5}\\)\\(2.\\ 10.9\\)\\(3.\\ 0.08\\)\\(4.\\ 6.25 = 6\frac{1}{4}\\)\\(5.\\ 4.125 = 4\frac{1}{8}\\)\\(6.\\ 0.075\\)

Explanation:

6. Converting 0.075 to a fraction

Step1: Identify the place value

The decimal 0.075 has three decimal places, so we can write it as a fraction with denominator \(1000\) (since the third decimal place is the thousandths place). So, \(0.075=\frac{75}{1000}\).

Step2: Simplify the fraction

To simplify \(\frac{75}{1000}\), we find the greatest common divisor (GCD) of 75 and 1000. The factors of 75 are \(1, 3, 5, 15, 25, 75\) and the factors of 1000 are \(1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000\). The GCD of 75 and 1000 is 25. We divide both the numerator and the denominator by 25: \(\frac{75\div25}{1000\div25}=\frac{3}{40}\).

Answer:

\(\frac{3}{40}\)