Question

How do you write -0.32 as a fraction in lowest terms?

Answer 1

In the above question, the concept is based on converting decimal into fraction form. We need to convert into the fraction form and then further we need to reduce the fraction in lowest terms by finding equivalent numbers in which numerator and denominator should be as small as possible.

Complete step by step solution:
The above given number is a negative decimal number. These negative numbers with decimal points can be converted into fractions just like positive values only by adding a negative sign in front of the fraction.

A fraction is said to be in lowest form, if its numerator and denominator are relatively prime numbers which means that they have no common factors left other than 1.

So now we first need to convert into the form of fraction. So, we will multiply the number with 100 and divide the number with 100.

$$\- \dfrac{{0.32}}{{100}} \times 100 \\\ = - \dfrac{{32}}{{100}} \\\$$

Now further we need to reduce it until the only common factor left is 1. So, we can reduce it by calculating the Greatest common factor (GCF) of both the numerator and denominator.
The GCF of 32 and 100 is 4.

So, we will reduce the numerator and denominator with number 4.
$- \dfrac{{32}}{{100}} = - \dfrac{8}{{25}}$

Note: An important thing to note is that we use 100 to multiply the decimal number 0.32. The reason for this is that the decimal point is before two digits. So, to shift the decimal to point by two-digit places we multiply by 100 which has two zeros.