Question

Convert \[\dfrac{7}{{15}}\] into a decimal and a percent.

Answer 1

Hint: In decimal form of a number the whole number is separated from the fractional part by a decimal point and to convert a number to a percentage we express it as a fraction of 100.

Complete step-by-step answer:
In the decimal form the whole number and the fractional part are separated by a decimal point. In our case the fraction is \[\dfrac{7}{{15}}\]. To express this in the decimal form divide \[7\] by \[15\]. When \[7\] is divided by \[15\] the quotient is \[0\] and the fractional part is \[\dfrac{7}{{15}}\]. Hence the whole number here is \[0\] and the fractional part is \[\dfrac{7}{{15}}\].
\[\therefore \] \[\dfrac{7}{{15}}\] \[ = \] \[0.46\]
To convert a number to a percentage it needs to be expressed as a fraction of 100. That is the denominator of the fraction should be 100, as percentage means out of 100. So if we can express any number in the fraction form as \[\dfrac{x}{{100}}\] then it is equal to \[x\% \].
We have
 \[\dfrac{7}{{15}}\]
 It was found that
 \[\dfrac{7}{{15}} = 0.46\]
\[ \Rightarrow 0.46 = \dfrac{{46}}{{100}}\]
Hence it is in the form \[\dfrac{x}{{100}}\] then it is equal to \[x\% \].
\[ \Rightarrow 0.46 = \dfrac{{46}}{{100}} = 46\% \]
Hence, \[\dfrac{7}{{15}}\] can be expressed as a decimal as \[0.46\] and as a percentage as \[46\% \].

Note: Any fraction has two parts a numerator and a denominator. That is for any fraction \[\dfrac{a}{b}\] the numerator is \[a\] and the denominator is \[b\]. For example for the fraction \[\dfrac{5}{9}\], the numerator is \[5\] and the denominator is \[9\].