Question

Complete the table

Ratio	Fraction	Decimal	Percent
\[4:5\]
	\[2\dfrac{1}{5}\]
		0.125
			\[63\% \]

Answer 1

Hint:
We will use our basic knowledge of conversion to solve the question and find the missing places. We will use the method of decimal shifting to find decimals, fractions, and ratios. And to find the percentage, we will multiply either the fraction or the decimal by 100. Hence, filling all the rows one by one.

Complete step by step solution:
In the first row, we are given the ratio \[4:5\].
If the ratio is \[a:b\] , the fraction is given by \[\dfrac{a}{b}\] ,
Hence, if the ratio is \[4:5\] , the fraction is \[\dfrac{4}{5}\]
If the ratio is \[a:b\] , the decimal is given by completely dividing a by b
Hence, if the ratio is \[4:5\] , the decimal is \[\dfrac{4}{5}\]
\[ \Rightarrow \dfrac{4}{5} = 0.8\]
If the ratio is \[4:5\], the percentage is given by multiplying either the fraction or the decimal by 100, we get
$ \Rightarrow \dfrac{4}{5} \times 100 = 0.8 \times 100 = 80\% $
Hence, the first row is

\[4:5\]

\[\dfrac{4}{5}\]

0.8

\[80\% \]

In the second row, we are given the fraction as \[2\dfrac{1}{5}\]
If we are given a fraction as \[a\dfrac{b}{c}\] then the ratio is \[\dfrac{{(a \times c) + b}}{c}\]
Hence, for \[2\dfrac{1}{5}\] ,
\[ \Rightarrow 2\dfrac{1}{5} = \dfrac{{2 \times 5 + 1}}{5}\]
On simplification, we get
\[ \Rightarrow 2\dfrac{1}{5} = \dfrac{{11}}{5}\]
Hence, \[11:5\]is the ratio for the fraction.
If the ratio is \[a:b\] , the decimal is given by completely dividing a by b
Hence, if the ratio is \[11:5\] , the decimal is $\dfrac{{11}}{5}$
\[ \Rightarrow \dfrac{{11}}{5} = 2.2\]
If the ratio is \[11:5\] , the percentage is given by multiplying either the fraction or the decimal by 100, we get
$ \Rightarrow \dfrac{{11}}{5} \times 100 = 2.2 \times 100 = 220\% $
Hence, the second row is

\[11:5\]

\[2\dfrac{1}{5}\]

2.2

$220\% $

In the third row, we are given the decimal as 0.125.
To get the fraction, remove the decimal by multiplying and dividing the decimal by power of ten equal to the number of digits present after the decimal, in this case, the power of ten would be 3, that is
Multiplying and dividing by 1000, we get
\[ \Rightarrow \dfrac{{0.125 \times 1000}}{{1000}} = \dfrac{{125}}{{1000}}\]
On solving RHS, we get
\[ \Rightarrow \dfrac{{0.125 \times 1000}}{{1000}} = \dfrac{1}{8}\]
Hence, \[\dfrac{1}{8}\] is the fraction for the given decimal 0.125.

If the fraction is \[\dfrac{a}{b}\] then the ratio is given as \[a:b\].
Hence, for \[\dfrac{1}{8}\]
\[ \Rightarrow \dfrac{1}{8} = 1:8\]
The percentage is given by multiplying either the fraction or the decimal by 100, we get
\[ \Rightarrow \dfrac{1}{8} \times 100 = 0.125 \times 100 = 12.5\]
Hence, the third row is

\[1:8\]

\[\dfrac{1}{8}\]

0.125

\[12.5\% \]

In the fourth row, we are given the percentage as \[63\% \]
If the percentage is given as \[a\]the decimal is calculated by dividing it by 100, that is \[\dfrac{a}{{100}}\]
If the percentage is \[63\% \] , the decimal is
\[ \Rightarrow 63\% = \dfrac{{63}}{{100}}\]
So, we have
\[ \Rightarrow 63\% = 0.63\]
Since, \[\dfrac{{63}}{{100}}\]is already in the lowest form, this is the required fraction
If the fraction is given by \[\dfrac{a}{b}\] , then the ratio is \[a:b\] , hence
If the fraction is \[\dfrac{{63}}{{100}}\] , the ratio is \[63:100\]
Hence, the fourth row is,

\[63:100\]

\[\dfrac{{63}}{{100}}\]

0.63

\[63\% \]

The complete table looks like

\[4:5\]	\[\dfrac{4}{5}\]	0.8	\[80\% \]
\[11:5\]	\[2\dfrac{1}{5}\]	2.2	$220\% $
\[1:8\]	\[\dfrac{1}{8}\]	0.125	\[12.5\% \]
\[63:100\]	\[\dfrac{{63}}{{100}}\]	0.63	\[63\% \]

Hence, this is the final answer.

Note:
In these types of questions, it is not advisable to always follow the above procedure or stick to one procedure only, there are numerous ways to do the same and we should choose the way of conversion which is suitable at that time to save extra effort and time.