Question

What is \[0.9\] as a percent \[\& \] as a fraction OR mixed number?

Answer 1

Hint: Percent or Percentage \[(\% )\] is a number or ratio that can be expressed as a fraction of \[100\]. Meanwhile, the fraction is part of a whole number. Fractions are typically written as one number over another with a line in between — for example \[\dfrac{1}{4}\]. A mixed number is a number consisting of a whole number and a proper fraction — for example \[2\dfrac{1}{4}\] .

Complete step by step solution:
We are given \[0.9\] as a percent \[\& \] as a fraction OR mixed number
We need to find out the percent of a given number, we can use the following formula:
\[p(\% ) = \dfrac{x}{y} \times 100\]
Where:
\[x\]= Number for which percentage is to be found out;
\[y\]= Total or whole number of given data
1) Now using the given formula to find out percent of \[0.9\]:
\[ \Rightarrow p(\% ) = \dfrac{{0.9}}{1} \times 100\]
Dividing it by 1,
\[ \Rightarrow p(\% ) = 0.9 \times 100\]
Finally multiplying by \[100\], we can get:
\[ \Rightarrow p(\% ) = 90\% \]

2) To find out the fraction of a given number, we can use the following formula:
\[Fraction = \dfrac{{Number\,of\,Parts}}{{Total\,Parts}}\]
The easy way is to equally divide the top and bottom of the fraction by whole numbers.
Now using the given formula, \[0.9\] can be thought of as:
\[ \Rightarrow 0.9 = \dfrac{{0.9}}{1}\]
Multiplying both the numerator and denominator by \[10\], we get
\[ \Rightarrow 0.9 = \dfrac{{0.9 \times 10}}{{1 \times 10}}\]
Solving the above multiplication, we get fraction as follows:
\[ \Rightarrow 0.9 = \dfrac{9}{{10}}\]
Since, there is no whole number in the given fraction \[\dfrac{9}{{10}}\], it is a proper fraction, and there is no mixed fraction.

Therefore, the equivalent percentage of 0.9 is 90% and equivalent proper fraction of 0.9 is $\dfrac{9}{10}$.

Note:
1) Alternate way to find out the percentage is finding out the fraction first and then multiplying it by 100.
In the given sum, percent can be found out as follows:
Fraction = \[\dfrac{9}{{10}}\]
Multiplying it by 100,
\[ \Rightarrow Percent(\% ) = \dfrac{9}{{10}} \times 100\]
Solving the above multiplication, we get:
\[ \Rightarrow Percent(\% ) = 90\% \]
2) Remember to use “\[\% \]” sign after finding out the percentage.
3) Every mixed number contains a fraction but every fraction is not a mixed number.