Question

How do you convert \[\dfrac{1}{9}\] into a decimal?

Answer 1

Hint: Fraction and decimal are kind off interconvertible terminologies, but one major significant contrast between them is that fractions tend to be a simple expression of ratios of whole numbers, but conversely decimal may be used to express long complex and possibly infinite numbers such as the value of \[\pi \].

Complete step-by-step solution:
To change fractions into decimals, we merely have to divide the quotient by the divisor, that is we simply have to do a regular division of numerator and the denominator, the denominator becomes the quotient and the numerator becomes the divisor.
In the given question, numeral “\[1\]” is the numerator, so it becomes the divisor, and numeral” \[9\]” is the denominator, and it becomes the quotient.
Also, since 9 is not a factor of any power of \[10\], so we cannot find an equivalent fraction,
So, \[\dfrac{1}{9}\]can also be written as \[1 \div 9\]
Further doing the division as shown below:
\[
  9\mathop{\left){\vphantom{1{1.0000}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{1.0000}}}}
\limits^{\displaystyle \,\,\, {0.111...}} \\
  \,\,\,\,\,\dfrac{0}{{10}} \\
  \,\,\,\,\,\dfrac{9}{
  10 \\
  \dfrac{9}{
  10 \\
  \dfrac{9}{{10}} \\
 } \\
 } \\
 \]
So, the answer for this question is \[0.111....\]
Also, this \[0.111....\] can also be written as \[0.\overline 1 \]

Additional information: So, to convert decimal into percentage we multiply the decimal from \[100\], and to convert a percentage into a decimal we divide the percent by \[100\].

Note: We have written \[0.111....\] as \[0.\overline 1 \]. This line above the numeral one is called a bar , this is a notation used in mathematics to represent infinity ,bar notation is an easier way to write a repeating number by putting a line, or bar, over the repeating numbers.