Question

$2.09$ can be expressed in terms of a percentage as
A) $0.29$
B) $0.029$
C) $209$
D) $20.9$

Answer 1

Hint:
Here, we will check each option one by one. We will first divide the number given in option by 100 and write it in fraction form. Then we will remove the decimal point by multiplying and dividing by 100. Then we will again convert the obtained fraction into a decimal number to check if it is equal to the given decimal number or not.

Complete step by step solution:
We will check which of the given options is equivalent to $2.09$.
A) Given $0.29\% $. We can write this as
$0.29\% = \dfrac{{0.29}}{{100}}$
We have to remove the decimal point from the numerator. For this, we will multiply and divide by 100, since there are 2 decimal places in 0.29. So,
 $\dfrac{{0.29}}{{100}} \times \dfrac{{100}}{{100}} = \dfrac{{29}}{{10000}}$.
This is already in the simplest form. Let us convert the fraction to decimal. We get
$\dfrac{{29}}{{10000}} = 0.0029$.
This is not equal to $$2.09$$. So, A is not the correct option.

B) Given $0.029\% $. We can write this as
$0.029\% = \dfrac{{0.029}}{{100}}$.
Since there are 3 decimal places in 0.029, we multiply and divide by 1000. So,
$\dfrac{{0.029}}{{100}} \times \dfrac{{1000}}{{1000}} = \dfrac{{29}}{{100000}}$.
This is already in the simplest form. Converting the fraction to decimal, we get
$\dfrac{{29}}{{100000}} = 0.00029$.
This is not equal to $2.09$. Thus, B is not the correct option.

C) Given $209\% $. We can write this as
$209\% = \dfrac{{209}}{{100}}$.
The numerator is a whole number. Also, the fraction is in the simplest form. Converting into decimal, we get
$\dfrac{{209}}{{100}} = 2.09$
This is equal to $2.09$. Hence, C is the correct option.

D) Given $20.9\% $. We can write this as
$20.9\% = \dfrac{{20.9}}{{100}}$.
Since 20.9 has only one decimal place, we will multiply and divide by 10. We get
$\dfrac{{20.9}}{{100}} \times \dfrac{{10}}{{10}} = \dfrac{{209}}{{1000}}$.
This is in the simplest form. Converting to decimal, we have
$\dfrac{{209}}{{1000}} = 0.209$
 This is not equal to $2.09$. Thus, D is not the correct option.

From the above discussion, we see that $2.09$ is equivalent to $209\% $ and thus, the correct option is C.

Note:
We can also solve the above problem by simply multiplying the given value by 100 to convert it into a percentage. We are given $2.09$, multiplying this by 100, we get
$2.09$ = $2.09 \times 100 = 209 \% $.
To convert a percentage to a fraction, we must divide the given percentage by 100. If the percentage is a decimal number, we have to remove the decimal point and convert the percentage to a whole number. Finally, we must reduce the resulting fraction into the simplest form.