Question

How do write $$6{\displaystyle \frac{15}{25}}$$ into a percent, and decimal?

Answer 1

Hint: From the given question we are given to write $$6{\displaystyle \frac{15}{25}}$$in percent, and as a decimal. As we all know that for 1=100% .For converting the $$6{\displaystyle \frac{15}{25}}$$ in percent we have to multiply it with 100%. To convert a fraction in decimal, one should make the denominator a power of 10. Here as the denominator is 25, we can easily do it by multiplying numerator and denominator by 4.

Complete step by step answer:
From the given question, we are given to write $$6{\displaystyle \frac{15}{25}}$$ as a percent as well as decimal.
By observing the question it is given that to write $$6{\displaystyle \frac{15}{25}}$$as a percent as well as decimal. So first of all let us convert the given fraction into percentage.
Let us consider
$$a=6{\displaystyle \frac{15}{25}}........\left(1\right)$$
First of all let us convert the mixed fraction in equation into proper fraction
$$\begin{array}{rl}& a={\displaystyle \frac{6\times 25+15}{25}}\\ & \Rightarrow a={\displaystyle \frac{165}{25}}\end{array}$$
Let us consider
$$\Rightarrow a={\displaystyle \frac{165}{25}}.........\left(2\right)$$
As we all know that every 1 = 100%.
So, for equation (1) in percent we have to multiply with 100 percent.
$$\begin{array}{rl}& \Rightarrow a\times 100\mathrm{\%}={\displaystyle \frac{165}{25}}\times 100\mathrm{\%}\\ & \Rightarrow a\mathrm{\%}=660\mathrm{\%}\end{array}$$
Let us consider
$$a\mathrm{\%}=660\mathrm{\%}.......(3)$$
Therefore, equation (3) is the percentage of equation (1).
Now let us find the decimal form of equation (1).
To convert a fraction in decimal, one should make the denominator a power of 10. Here as the denominator is 25, we can easily do it by multiplying numerator and denominator by 4.
Multiplying numerator and denominator by 4.
$$a={\displaystyle \frac{165}{25}}$$
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{165\times 4}{25\times 4}}\\ & \Rightarrow {\displaystyle \frac{660}{100}}\\ & \Rightarrow 6.60\end{array}$$
 So, let us consider
$$b=6.60..........\left(4\right)$$
Therefore a and b are the percentage and decimal values of equation (1) respectively.

Note:
Students should be well aware of linear equation concepts. Examiners may ask to convert some improper fractions to decimal. So students should be aware of these types of concepts also. Students should avoid calculation mistakes while doing this problem.