Convert 0.33 into $\frac{p}{q}$ form

Question

Accepted Answer

The correct option is 4:
To convert the decimal $0.33$ into $\frac{p}{q}$ form, we first need to identify if it's a terminating decimal or a repeating decimal. In this case, the question shows $0.33$ without a bar over the numbers, which usually indicates that it is a terminating decimal. However, given the options and the correct answer being $\frac{1}{3}$, it implies that $0.33$ is a shorthand for the repeating decimal $0.333...$.

Let $x = 0.333...$ (Equation 1)
Since there is one repeating digit (3), we multiply both sides of Equation 1 by $10^1 = 10$.
$10x = 3.333...$ (Equation 2)

Now, subtract Equation 1 from Equation 2:
$10x - x = 3.333... - 0.333...$
$9x = 3$
$x = \frac{3}{9}$
Simplify the fraction:
$x = \frac{1}{3}$

Thus, $0.333...$ in $\frac{p}{q}$ form is $\frac{1}{3}$.

The incorrect option is 1:
$\frac{33}{100}$ represents the terminating decimal $0.33$, not the repeating decimal $0.333...$.

The incorrect option is 2:
$\frac{10}{3}$ is equivalent to $3.333...$, which is not $0.333...$.

The incorrect option is 3:
$\frac{3}{10}$ is equivalent to $0.3$, which is not $0.333...$.