Solve $0.5 \times 0.05$.

Hint: To solve such a question start by converting each number in the given term into their corresponding fraction. Then multiply the two fraction terms together. After obtaining the result in fraction convert it back into the decimal term.

Complete step-by-step solution:
It is given $0.5 \times 0.05$. Here it is asked to solve the given term.
First, write each number in the given term in fraction form. That is,
$\Rightarrow$$0.5 = \dfrac{{0.5}}{1}$
Multiply both numerator and denominator of RHS with $10$, that is,
$\Rightarrow$$0.5 = \dfrac{{0.5 \times 10}}{{1 \times 10}}$
Simplifying further we get,
$\Rightarrow$$0.5 = \dfrac{5}{{10}}$
Next, consider the other number. That is,
$\Rightarrow$$0.05 = \dfrac{{0.05}}{1}$
Multiply both numerator and denominator of RHS with $100$, that is,
$\Rightarrow$$0.05 = \dfrac{{0.05 \times 100}}{{1 \times 100}}$
Simplifying further we get,
$\Rightarrow$$0.05 = \dfrac{5}{{100}}$
Therefore,
$\Rightarrow$$0.5 \times 0.05 = \dfrac{5}{{10}} \times \dfrac{5}{{100}}$
Simplifying further we get,
$\Rightarrow$$0.5 \times 0.05 = \dfrac{{25}}{{1000}}$
Converting this into decimal form, we get
$\Rightarrow$$0.5 \times 0.05 = 0.025$

Hence the solution of $0.5 \times 0.05$ is $\;0.025$.

Note: Proper fraction can be defined as a fraction whose numerator is less than the denominator. An improper fraction can be defined as a fraction whose numerator is greater than the denominator. When we multiply a proper or an improper fraction with a whole number we have to multiply the whole number with the numerator of the fraction, and should not change the denominator. While multiplying a mixed fraction with the whole number, we have to first convert the mixed fraction into an improper fraction and then multiply with the whole number.