Question

How do you convert \[ - 0.125\] into a fraction and percent?

Answer 1

Hint: For converting the given number into a fraction, we have to write it in the form of an equation by equating it to some variable. Then, we have to multiply the equation repeatedly by \[10\] until we remove the decimal point and convert the given number into a whole number. On solving this equation, we will obtain the required fraction form of the given number. For converting the given number into percent, we simply have to multiply the given number by \[100\].

Complete step-by-step solution:
According to the question, we have the number \[ - 0.125\] which has to be converted into a fraction and percentage. Let us equate the given number to a variable, say \[n\], so that we can write the below equation
\[n = - 0.125\]
Now, for converting the given number to a fraction, we need to multiply it by \[10\] repeatedly until we obtain zero after the decimal.
So, multiplying both sides of the above equation with \[10\], we get
\[\begin{array}{l} \Rightarrow 10n = - 0.125 \times 10\\ \Rightarrow 10n = - 1.25\end{array}\]
As we can see, the decimal is still not removed, so multiplying the above equation by \[10\], we get
\[\begin{array}{l} \Rightarrow 100n = - 1.25{\kern 1pt} \times 10\\ \Rightarrow 100n = - 12.5\end{array}\]
We can see that the decimal is still not removed, so we will again multiply the above equation by \[10\] to get
\[\begin{array}{l} \Rightarrow 1000n = - 12.5{\kern 1pt} \times 10\\ \Rightarrow 1000n = - 125\end{array}\]
Thus, we have obtained zero after the decimal. Now, we divide both sides of the above equation by \[1000\] to get
\[ \Rightarrow n = - \dfrac{{125}}{{1000}}\]…………………………….\[\left( 1 \right)\]
On simplifying the RHS, we finally get
\[ \Rightarrow n = - \dfrac{1}{8}\]
Hence, the given number is converted to the fractional form as \[ - \dfrac{1}{8}\].
Now, we know that for converting a number to percent, we have to multiply it by \[100\].
So on multiplying equation \[\left( 1 \right)\] by 100, we get
\[ \Rightarrow n = - \dfrac{{125}}{{1000}} \times 100 = - 12.5\% \]

Therefore, we get the percentage as \[ - 12.5\% \].

Note:
There are three main types of fractions i.e. proper fractions, improper fractions, and mixed fractions. A proper fraction is a fraction having the numerator less or lowers in degree, than the denominator. The value of proper fraction after simplification is always less than 1. An improper fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction. A mixed Fraction is the combination of a natural number and fraction. The percentage can be represented as both decimal and fraction.