Question

How do you write 1.8 as a fraction and as a percent?

Answer 1

Hint: To convert a decimal number to fraction form, we have to get rid of its decimal point. To do this we will multiply and divide the number with \[{{n}^{th}}\] power of 10 where \[n\] is the number of digits after its decimal point. After this, we have to convert the obtained fraction to its simplest form. Now, to write the fraction as a percent, we have to find a number whose product with denominator equals 100, this can be easily found by dividing 100 by the denominator. After we got this value, the percent form is the product of this value and numerator. Assume that we have a fraction in its simplest form as \[\dfrac{a}{b}\], to write this as percent, we have to multiply the numerator by \[\dfrac{100}{denominator}\]
\[\Rightarrow a\times \dfrac{100}{b}=\dfrac{100a}{b}\] is the percent form of fraction \[\dfrac{a}{b}\].

Complete step by step answer:
We are given the decimal number 1.8 and have to write it as fraction and percent. First, to convert into fraction form, we will multiply and divide the number with \[{{n}^{th}}\] power of 10 where \[n\] is the number of digits after its decimal point. 1.8 have only one digit after the decimal point, so we multiply and divide 1.8 by \[{{10}^{1}}\], we get
\[\Rightarrow 1.8\times \dfrac{{{10}^{1}}}{{{10}^{1}}}=\dfrac{1.8\times 10}{10}=\dfrac{18}{10}\]
To convert this into the simplest form, we divide both numerator and denominator by their largest common factor, as we can see the largest common factor 10 and 18 have is 2. So, the simplest form will be
\[\Rightarrow \dfrac{\dfrac{18}{2}}{\dfrac{10}{2}}=\dfrac{9}{5}\]
This is how 1.8 is written as a fraction.
Now we know that, given a fraction \[\dfrac{a}{b}\], it can be written as percent by multiplying the numerator by \[\dfrac{100}{denominator}\], which means percent form will be \[\dfrac{100}{b}\times a=\dfrac{100a}{b}\]
for this problem, the fraction is \[\dfrac{9}{5}\], so in percent form it is written as
\[\Rightarrow \dfrac{100}{5}\times 9=\dfrac{100\times 9}{5}\]
\[\Rightarrow 180\]

As this is a percent, it should be written as \[180\%\].

Note: By simply remembering how the steps any decimal number can be written in its fraction and percent form. These types of problems are not too difficult but there is a possibility of making calculation mistakes, so it should be avoided. Don’t forget to give the \[\%\] after the percent form, else the answer will become incorrect.