Question

How do you write the fraction \[\dfrac{{29}}{7}\] as a repeating decimal?

Answer 1

Hint: Here we will firstly modify the given fraction such that its numerator is splitted into two terms one of which is the height multiple of 7. Then we will apply a simple division operation to get the decimal form of the given fraction.

Complete Step by Step Solution:
The fraction is \[\dfrac{{29}}{7}\].
Firstly we will modify the given fraction so that the numerator of the given fraction will get divided into two terms in which one term will be the highest multiple of 7. Therefore, we get
\[ \Rightarrow \dfrac{{29}}{7} = \dfrac{{28 + 1}}{7}\]
\[ \Rightarrow \dfrac{{29}}{7} = \dfrac{{28}}{7} + \dfrac{1}{7}\]
Now after solving the above equation, we get
\[ \Rightarrow \dfrac{{29}}{7} = 4 + \dfrac{1}{7}\]
Now by simply division operation we will get the decimal form of the fraction \[\dfrac{1}{7}\]. Therefore, we get
\[ \Rightarrow \dfrac{{29}}{7} = 4 + 0.14285714285714\]
\[ \Rightarrow \dfrac{{29}}{7} = 4 + 0.\overline {142857} \]
Now we will simply add the numbers. Therefore, we get
\[ \Rightarrow \dfrac{{29}}{7} = 4.\overline {142857} \]

Hence, the fraction \[\dfrac{{29}}{7}\] as a repeating decimal is equal to \[4.\overline {142857} \].

Note:
Any number can be represented in decimal form. We do not need to write whole numbers in decimal form because it is already implied. For example, 34.00 can simply be written as 34. The fraction given in our question is of proper fraction. We should know the basic three types of fraction. When the decimal digits starts to repeat itself then we will simply put the bar on the repeating digits.
We know the definition of three main types of fraction i.e. proper fractions, improper fractions and mixed fractions.
Proper fractions are a fraction having the numerator less, or lower in degree, than the denominator i.e., \[Numerator < Denominator\]. The value of proper fraction after simplification is always less than 1.
Improper Fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction i.e., \[Numerator \to Denominator\]. After the simplification of an improper fraction results in the value which is equal or greater than 1, but not less than 1.
Mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1. An improper fraction can be converted into a mixed fraction.