Question

What is $-4.45$ as a fraction in simplest form?

Answer 1

Hint: Any decimal number can be expressed as a fraction by multiplying and dividing 10 until there are no numbers to the right side of the decimal point. After this, we can simplify the fraction by finding the common factors in both the numerator and denominator and then cancelling them out. Repeating this process until there are no more common factors between the numerator and denominator yields the fraction of the given decimal number in simplest form.

Complete step by step answer:
The given number $-4.45$ has two numbers to the right of the decimal place, hence let us first multiply and divide 100 to convert it into a fraction.
$\begin{align}
  & -4.45=-\dfrac{4.45\times 100}{100} \\
 & -4.45=-\dfrac{445}{100} \\
\end{align}$
Now, we have obtained a fraction. Next we need to find the common factors and cancel them out from both numerator and denominator to express it as a simplified fraction. Splitting numerator and denominator into their factors, we get,
$\begin{align}
  & \,\,445=5\times 89 \\
 & \,\,100=5\times 20 \\
\end{align}$
Hence we can cancel out the common factor 5 in both the terms and we get,
$-4.45=-\dfrac{89}{20}$
We can clearly see that the terms 89 and 20 have no factors in common as 89 is a prime number and it cannot be further factorized. Hence the simplified fractional form of the given decimal number is $-\dfrac{89}{20}$.

Note: While solving this problem, one has to take the factors such that they can be cancelled out in both numerator and denominator. Since, only 5 was common in this problem there was no need to further factorize 20. This reduces the time needed to solve the problem and unwanted calculations.