Question

How do you write $4\dfrac{3}{5}$ as a percent?

Answer 1

Hint: The given number is in the fractional form. To convert the number to a percentage, one must first convert the fraction into a decimal value. From the decimal value, the percentage can be obtained by multiplying $\;100$ to the decimal value.

Complete step-by-step solution:
Here the number given is a combination of a whole integer and a fraction.
This can be understood as, here $\;4$ whole bodies are considered and $\;3$ parts out of $\;5$ parts of the fifth body are considered
To express this number in a simplified manner, we can convert it to decimal form.
Now, in decimal format, the whole integer is written on the left-hand side while the fractional part is written on the right-hand side of the point, which is known as a decimal point.
Now, we need to convert the fractional part $\dfrac{3}{5}$ to decimal form
In the decimal form, the denominator is a power of $\;10$ .
Here, we can make the denominator $\;10$ by multiplying $\;2$ to it.
Hence, multiplying $\;2$ to the numerator and denominator we get
$ \Rightarrow \dfrac{{3 \times 2}}{{5 \times 2}} = \dfrac{6}{{10}}$
As the power of $\;10$ in denominator is $\;1$ , we can say the number of values to be written after the decimal point is $\;1$ .
Hence we can give the decimal value as
$ \Rightarrow \dfrac{6}{{10}} = 0.6$
Now, from the given value, $\;4$ is a whole integer and it will be written on the left side of the decimal point, while the fractional part on the right side as follows
$ \Rightarrow 4\dfrac{3}{5} = 4.6$
Now, as we have got the decimal value, we can find the percentage value by multiplying $\;100$ to the decimal value
As we know that $\;100$ is a $\;10$ with the power $\;2$ .
Hence, multiplying $\;100$ to the decimal value shifts the decimal point by two places on the right side as follows,
$ \Rightarrow 4.6 \times 100 = 460.0$
By adding a percentage sign, we get the percent value of the fractional number

Hence the percent form of $4\dfrac{3}{5}$ is $460\% $

Note: To convert the fractional part to decimal, one can also divide $\;3$ by $\;5$ i.e. taking $\;3$ as dividend and $\;5$ as the divisor. We can directly convert the fraction to percent if the fraction is in the $\dfrac{p}{q}$ format. To convert the given number to this form, we calculate $p = (5 \times 4) + 3 = 23$ and $q = 5$.