Question

date 01/22/2026 period
lesson 1 skills practice
decimals and fractions
write each decimal as a fraction or mixed number in simplest form.

1. 0.6 = 3/5
2. 10.9
3. 0.08
4. 6.25 =
5. 4.125 =
6. 0.075

Explanation:

To solve the problem of converting \(0.075\) to a fraction in simplest form, we can follow these steps:

Step 1: Identify the place value of the decimal

The decimal \(0.075\) has three decimal places. This means it can be written as a fraction with a denominator of \(1000\) (since the third decimal place represents thousandths). So, we have:
\[
0.075=\frac{75}{1000}
\]

Step 2: Simplify the fraction

To simplify \(\frac{75}{1000}\), we find the greatest common divisor (GCD) of the numerator (\(75\)) and the denominator (\(1000\)). 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 \(25\):
\[
\frac{75\div25}{1000\div25}=\frac{3}{40}
\]

So, \(0.075\) as a fraction in simplest form is \(\frac{3}{40}\).

Answer:

To solve the problem of converting \(0.075\) to a fraction in simplest form, we can follow these steps:

Step 1: Identify the place value of the decimal

The decimal \(0.075\) has three decimal places. This means it can be written as a fraction with a denominator of \(1000\) (since the third decimal place represents thousandths). So, we have:
\[
0.075=\frac{75}{1000}
\]

Step 2: Simplify the fraction

To simplify \(\frac{75}{1000}\), we find the greatest common divisor (GCD) of the numerator (\(75\)) and the denominator (\(1000\)). 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 \(25\):
\[
\frac{75\div25}{1000\div25}=\frac{3}{40}
\]

So, \(0.075\) as a fraction in simplest form is \(\frac{3}{40}\).