Question

Express $0.3\overline{2}$ as a fraction in simplest form.

Answer 1

The repeating decimal $0.3\overline{2}$ is expressed as the fraction 1/3 by setting up an equation, manipulating it to remove the repeating part, and then simplifying the resulting fraction.

Step-by-step explanation:

To express the repeating decimal $0.3\overline{2}$ as a fraction, we follow these steps:

1. Let x equal the repeating decimal, x = 0.3\overline{2}.
2. Multiply x by 10 to shift the decimal point right before the repeating digit, 10x = 3.\overline{2}.
3. Subtract the original equation (x) from the new one (10x) to cancel out the repeating part: 10x - x = 3.\overline{2} - 0.3\overline{2}.
4. This gives us 9x = 3, where we divide both sides by 9 to isolate x: x = 3/9.
5. Simplify the fraction to get the simplest form, which is 1/3.

Therefore, $0.3\overline{2}$ as a fraction in simplest form is 1/3.

Answer 2

3/20

Step-by-step explanation:

`(0.3)/(2)=(0.3*10)/(2*10)=(3)/(20)`