Question

How do you write $0.\;033$ as a fraction?

Answer 1

Hint: To solve such questions first understand the meaning of fractions. A fraction can be defined as a number that is written in the form of $\dfrac{a}{b}$. Here $a$ and b are the numerator and denominator respectively. A proper fraction is that fraction whose numerator will be less than that of its denominator.

Complete step-by-step solution:
The given number is $0.\;033$.
It is asked to write it as a fraction.
If the given number is to be written as a fraction over ten, then it would be as shown below
$\Rightarrow$$\dfrac{{0.033}}{1} \times \dfrac{{10}}{{10}} = \dfrac{{0.33}}{{10}}$.
If the given number is to be written as a fraction over a hundred, then it would be as shown below
\Rightarrow$$\dfrac{{0.033}}{1} \times \dfrac{{100}}{{100}} = \dfrac{{3.3}}{{100}}$.
If the given number is to be written as a fraction over a thousand, then it would be as shown below
\Rightarrow$$\dfrac{{0.033}}{1} \times \dfrac{{1000}}{{1000}} = \dfrac{{33}}{{1000}}$

Therefore, the number $0.\;033$ can be expressed as $\dfrac{{33}}{{1000}}$ as a fraction.

Additional Information: Simple fractions are those whose denominator and numerator are whole numbers. Complex fractions are those fractions whose denominator and numerator are itself a fraction.
When more than one fraction has the same denominator then those fractions are called fractions.
When more than one fraction has a different denominator then those fractions are called, unlike fractions.

Note: Another way to write in the form of a fraction is to expand the given number. The expanded form of the given number can be written as
$0.033 = 0 \times 1 + 0 \times \dfrac{1}{{10}} + 3 \times \dfrac{1}{{100}} + 3 \times \dfrac{1}{{1000}}$.
From the expanded form it can be seen that to write the decimal number $0.\;033$ as a fraction we have to move three decimals places to the right.