In this chapter, we will learn to convert rational number into decimal numbers with examples.
At the end of the chapter, some problems are also given for your practice.
How to convert rational number into decimals ?
We know that rational numbers are represented in the form of fraction \mathtt{\ \frac{p}{q}} .
Where both p and q are integers.
To convert the rational number into decimals, simply divide the numerator and denominator and write the quotient as a result.
Note that after division, you will get two type of decimals;
(a) Terminating decimals
This decimal value will terminate after some digits.
(b) Non terminating decimals
The decimals with infinite number of digits. In this case, we will take approximate value of the quotient.
But why we are converting rational number into decimal in first place ?
Because doing mathematical operations like addition/subtraction is much easier than the rational numbers.
In higher mathematics, you will be asked to solve complex math problems. Doing math calculations using decimal number will be much easier and time saving.
Examples of Rational number to decimal number conversion
Given below are examples of writing rational numbers in decimal form.
Example 01
Convert 2/5 into decimal.
Solution
Divide numerator by denominator.
\mathtt{\frac{2}{5} \Longrightarrow \ 0.4}
Hence, the rational number is converted into terminating decimal.
Example 02
Convert 12 / 3 into decimal number.
Solution
\mathtt{\frac{12}{3} \Longrightarrow \ 4.0}
Here we again get terminating decimal.
Example 03
Convert 100/3 into decimal form.
Solution
\mathtt{\frac{100}{3} \Longrightarrow \ 33.3333…….}
Here we get non terminating decimal.
Here we will take the approximate value of 33.33 as a solution.
Example 04
Convert 50/7 in decimal form.
Solution
Dividing numerator by denominator.
\mathtt{\ \frac{50}{7} \Longrightarrow \ 7.14285714286}
Note that the given solution has too many decimal places. It will be convenient to take the approximate value of the number.
⟹ 7.14285714286
⟹ 7.14 (approx.)
Hence, 7.14 is the solution.
Example 05
Convert 12/5 into rational number.
Solution
Dividing numerator by denominator.
\mathtt{\ \frac{12}{5} \Longrightarrow \ 2.4}
Hence, 2.4 is the solution.
I hope you understood the above examples. Given below are some problems for practice.
Rational number to decimals – Solved Problems
(01) Convert the given rational numbers into decimals. Check if the resulting decimal is terminating or non – terminating.
(a) 11/5
(b) 100/6
(c) 13 / 7
(d) 8 / 9
(e) 50 / 2
(f) 75 / 10
(g) 69 / 11
(h) 14 / 4
(i) 18 / 9
(j) 105 / 7
Solution
To convert the given rational number in decimal form, simply divide numerator by denominator.
(a) 11/5
\mathtt{\frac{11}{5} \Longrightarrow \ 2.2}
Here 2.2 is a terminating decimal.
(b) 100/6
\mathtt{\frac{100}{6} \Longrightarrow \ 16.6666.\ .\ .\ .}
Here 16.6666. . . . . is a non terminating decimal.
We will take the approximate value of given number.
\mathtt{16.6666.\ .\ .\ \approx \ 16.67}
(c) 13 / 7
\mathtt{\frac{13}{7} \Longrightarrow \ 1.85714285714}
Taking approximate value.
\mathtt{1.85714285714\ \approx \ 1.86}
(d) 8 / 9
\mathtt{\frac{8}{9} \Longrightarrow \ 0.8888\ .\ .\ .\ .}
It’s a non terminating decimal.
Taking approximate value.
\mathtt{0.8888\ .\ .\ .\ \approx \ 0.89}
(e) 50 / 2
\mathtt{\frac{50}{2} \Longrightarrow \ 25.0}
It’s a terminating decimal.
(f) 75 / 10
\mathtt{\frac{75}{10} \Longrightarrow \ 7.5}
It’s a terminating decimal.
(g) 69 / 11
\mathtt{\frac{69}{11} \Longrightarrow \ 6.272727\ .\ .\ .}
It’s a non terminating decimal.
Taking approximate value;
\mathtt{6.272727\ .\ .\ .\approx \ 6.27}
(h) 14 / 4
\mathtt{\frac{14}{4} \Longrightarrow \ 3.5}
It’s a terminating decimal.
(i) 18 / 9
\mathtt{\frac{18}{9} \Longrightarrow \ 2.0}
It’s a terminating decimal.
(j) 105 / 7
\mathtt{\frac{105}{7} \Longrightarrow \ 15}
It’s a terminating decimal.
Next chapter : Terminating and non terminating rational number