Question

The decimal form of \[\dfrac{9}{1000}\] is
(a) 0.9
(b) 1000.9
(c) 0.009
(d) 0.09

Answer 1

Hint: \[\dfrac{9}{1000}\] can also be written as \[9\div 1000\]. Thus by long division find the quotient. The remainder will be zero. The quotient will give the decimal form of the fraction.

Complete step-by-step solution -

We know that a fraction is made up of two parts: a numerator and a denominator. It is used to represent how many parts we have out of the total number of parts. We have been given the fraction \[\dfrac{9}{1000}\]. Out of which 9 is the numerator and 1000 is the denominator.
The line in a fraction that separates the numerator and denominator can be rewritten using a division symbol.
i.e. \[\dfrac{9}{1000}\] can be written as \[9\div 1000\].
So, to convert a fraction to a decimal, divide the numerator by the denominator. Now let us divide \[9\div 1000\] by a long division method. Here 9 is the dividend and 1000 is the divisor.
\[1000\overset{0.009}{\overline{\left){\begin{align}
  & 9.000 \\
 & \underline{-0} \\
 & 90 \\
 & \underline{-0} \\
 & 900 \\
 & \underline{-0} \\
 & 9000 \\
 & \underline{-9000} \\
 & 0 \\
\end{align}}\right.}}\]
Thus, \[9\div 1000=0.009\].
Insert a decimal point in the quotient, exactly above the decimal point in the number under the division bar.
Here, 1000 is a 4 digit number, where 9 is a one digit number. So, in order to divide use decimals given as above.
Thus we got, \[9\div 1000=0.009\]
i.e. \[\dfrac{9}{1000}=0.009\].
Thus, the decimal form of \[\dfrac{9}{1000}\] is \[0.009\].
\[\therefore \] Option (c) is the correct answer.

Note: To find the decimal form of \[\dfrac{9}{1000}\] it is not necessary to use long division.
We know that \[\dfrac{1}{1000}=0.001\]. Similarly, \[\dfrac{9}{1000}=0.009\].
We can see other examples like \[\dfrac{9}{10}=0.9\] and \[\dfrac{9}{100}=0.09\]. If the denominator is the 10, 100, 1000 etc, the decimal conversion is simple.