Answer
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Hint: The ratio can be written in the form as numerator: denominator and vice versa for the fraction conversion. To obtain the decimal form, we just have to divide the numerator by denominator. And to get the percent term we have to multiply the decimal term by 100. An improper fraction is called when the numerator in the fraction is greater than the denominator.
Complete step-by-step answer:
Let us consider the first row.
In the first row, the ratio given is 4:5.
As we can see that 4 is not further divisible by 5 we can simply write down the ratio in the form of $\dfrac{\text{Numerator}}{\text{Denominator}}$.
Therefore, the fraction of the given ratio is $\dfrac{4}{5}$.
Moving on further, in order to get the decimal term of the same fraction we need to divide 4 by 5.
The division is shown as follows,
$5\overset{0.8}{\overline{\left){\begin{align}
& \,\,\,\,4 \\
& \dfrac{-0}{\,\,\,40} \\
& \dfrac{-40}{\,\,0} \\
\end{align}}\right.}}$
Therefore, in this, the quotient term is the decimal term and the remainder is 0.
Hence, the decimal term is 0.8………………(i)
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (i) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 0.8=80%$.
Therefore, the percentage term is 80%.
Let's consider the second row now.
The given element in the second row is a fraction $2\dfrac{1}{5}$.
The given fraction is improper. First, we need to convert into the proper fraction.
The improper fraction of the form $a\dfrac{b}{c}$ can be converted as $\dfrac{a\times c+b}{c}$.
Using the above form and converting into a proper fraction we get,
$2\dfrac{1}{5}=\dfrac{11}{5}$……….(ii)
The ratio term can be given as numerator: denominator.
Therefore, The ratio term is 11:5.
Moving on further, in order to get the decimal term of the same fraction we need to divide 11 by 5.
The division is shown as follows,
\[5\overset{2.2}{\overline{\left){\begin{align}
& \,\,\,\,11 \\
& \dfrac{-10}{\,\,\,10} \\
& \dfrac{-10}{\,\,0} \\
\end{align}}\right.}}\]
Therefore, in this, the quotient term is the decimal term and the remainder is 0.
Hence, the decimal term is 2.2………………(iii)
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (iii) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 2.2=220%$.
Therefore, the percentage term is 220%.
Let's consider the third term.
The given element is the decimal term as 0.125……….(iv)
The main aim is to remove the decimal term so let us multiply in numerator and denominator by 1000.
We get, $\dfrac{0.125\times 1000}{1\times 1000}=\dfrac{125}{1000}$
Lets simply get a simpler fraction.
$\dfrac{125}{1000}\Rightarrow \dfrac{1}{2\times 2\times 2}\Rightarrow \dfrac{1}{8}$.
Therefore the fraction term is $\dfrac{1}{8}$.
The ratio term can be given as numerator: denominator.
Therefore, the ratio term is 1:8.
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (iv) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 0.125=12.5%$.
Therefore, the percentage term is 12.5%.
Let's consider the last row.
The given percent term is 63%
Just by dividing by 100, we can get the decimal term.
Therefore, decimal term $=\dfrac{63}{100}=0.63$
63 is not divisible by 100. So, we have to keep the fraction as it is. Hence, the fraction term is $\dfrac{63}{100}$.
The ratio term can be given as numerator: denominator.
Therefore, the ratio term is 63:100.
The final table looks like as follows,
Note: It is easily mistaken while converting from fraction to decimal form that the numerator is the number that is to divide by the denominator and not the vice versa. Also, it is important to convert the improper fraction into a proper fraction or else the answer can get wrong.
Complete step-by-step answer:
Let us consider the first row.
In the first row, the ratio given is 4:5.
As we can see that 4 is not further divisible by 5 we can simply write down the ratio in the form of $\dfrac{\text{Numerator}}{\text{Denominator}}$.
Therefore, the fraction of the given ratio is $\dfrac{4}{5}$.
Moving on further, in order to get the decimal term of the same fraction we need to divide 4 by 5.
The division is shown as follows,
$5\overset{0.8}{\overline{\left){\begin{align}
& \,\,\,\,4 \\
& \dfrac{-0}{\,\,\,40} \\
& \dfrac{-40}{\,\,0} \\
\end{align}}\right.}}$
Therefore, in this, the quotient term is the decimal term and the remainder is 0.
Hence, the decimal term is 0.8………………(i)
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (i) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 0.8=80%$.
Therefore, the percentage term is 80%.
Let's consider the second row now.
The given element in the second row is a fraction $2\dfrac{1}{5}$.
The given fraction is improper. First, we need to convert into the proper fraction.
The improper fraction of the form $a\dfrac{b}{c}$ can be converted as $\dfrac{a\times c+b}{c}$.
Using the above form and converting into a proper fraction we get,
$2\dfrac{1}{5}=\dfrac{11}{5}$……….(ii)
The ratio term can be given as numerator: denominator.
Therefore, The ratio term is 11:5.
Moving on further, in order to get the decimal term of the same fraction we need to divide 11 by 5.
The division is shown as follows,
\[5\overset{2.2}{\overline{\left){\begin{align}
& \,\,\,\,11 \\
& \dfrac{-10}{\,\,\,10} \\
& \dfrac{-10}{\,\,0} \\
\end{align}}\right.}}\]
Therefore, in this, the quotient term is the decimal term and the remainder is 0.
Hence, the decimal term is 2.2………………(iii)
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (iii) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 2.2=220%$.
Therefore, the percentage term is 220%.
Let's consider the third term.
The given element is the decimal term as 0.125……….(iv)
The main aim is to remove the decimal term so let us multiply in numerator and denominator by 1000.
We get, $\dfrac{0.125\times 1000}{1\times 1000}=\dfrac{125}{1000}$
Lets simply get a simpler fraction.
$\dfrac{125}{1000}\Rightarrow \dfrac{1}{2\times 2\times 2}\Rightarrow \dfrac{1}{8}$.
Therefore the fraction term is $\dfrac{1}{8}$.
The ratio term can be given as numerator: denominator.
Therefore, the ratio term is 1:8.
We can get the percent term by just multiplying the decimal term by 100.
Therefore, multiplying equation (iv) by 100 we get,
Percentage $=100\times \text{Decimal term}$.
Percentage $=100\times 0.125=12.5%$.
Therefore, the percentage term is 12.5%.
Let's consider the last row.
The given percent term is 63%
Just by dividing by 100, we can get the decimal term.
Therefore, decimal term $=\dfrac{63}{100}=0.63$
63 is not divisible by 100. So, we have to keep the fraction as it is. Hence, the fraction term is $\dfrac{63}{100}$.
The ratio term can be given as numerator: denominator.
Therefore, the ratio term is 63:100.
The final table looks like as follows,
Ratio | Fraction | Decimal | Fraction |
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% |
Note: It is easily mistaken while converting from fraction to decimal form that the numerator is the number that is to divide by the denominator and not the vice versa. Also, it is important to convert the improper fraction into a proper fraction or else the answer can get wrong.
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