Question

How do you convert $0.0112$ to a fraction?

Answer 1

Hint: The conversion of numbers from fraction to decimal and that of decimal to fraction is done by simple division or multiplication of the given numbers by ten, hundred, thousand, etc according to the requirements of the number given. Here, we shall convert the given decimal number to fraction by multiplying it by 10 raised to power equal to the number of significant digits after the decimal point and we shall simplify the fraction obtained.

Complete step-by-step solution:
In $0.0112$, we shall first analyze the positions of all the digits after the decimal point.
Here, 0 is at the tenths place, therefore we can also write is as $\dfrac{0}{10}$.
The first 1 is at the hundredths place, therefore it can be written as $\dfrac{1}{100}$.
The second 1 is at the thousandths place, therefore it can be written as $\dfrac{1}{1000}$ and lastly the digit 2 is at the ten-thousandths place, hence it can be written as $\dfrac{2}{10000}$.
Since the decimal number is comprised of all these digits, thus we shall sum their fractional representations to find the final fraction.
$\Rightarrow 0.0112=\dfrac{0}{10}+\dfrac{1}{100}+\dfrac{1}{1000}+\dfrac{2}{10000}$
Now, taking LCM in the denominator and multiplying the numerators with the same terms respectively, we get
$\Rightarrow 0.0112=\dfrac{0}{10}\times \dfrac{1000}{1000}+\dfrac{1}{100}\times \dfrac{100}{100}+\dfrac{1}{1000}\times \dfrac{10}{10}+\dfrac{2}{10000}$
$\Rightarrow 0.0112=\dfrac{0+100+10+2}{10000}$
$\Rightarrow 0.0112=\dfrac{112}{10000}$
The fraction obtained is not in its simplest form, therefore, we shall cancel the common factor 16 from numerator and denominator and we get,
$\Rightarrow 0.0112=\dfrac{7}{625}$
Therefore, the fractional form of $0.0112$ is $\dfrac{7}{625}$.

Note: Sometimes, we tend to forget to cancel the common factors from the numerator and denominator of a fractional term. However, the proper representation of a fraction is only in its simplest form. The simplest form of any fractional term is the one in which there are no common factors in the numerator and denominator.