Question

Find the value of \[0.0\overline {37} \], where \[0.0\overline {37} \] stands for the number \[0.0373737...\] .
A.\[\dfrac{{37}}{{1000}}\]
B. \[\dfrac{{37}}{{990}}\]
C. \[\dfrac{1}{{37}}\]
D. \[\dfrac{1}{{27}}\]

Answer 1

Hint: It is given that the value of \[0.0\overline {37} \] is \[0.0373737...\] and we have to obtain the number which gives \[0.0\overline {37} \] as its value. Suppose that the given number is x. Then obtain the value of \[1000x\] and \[10x\]. Subtract 10x from 1000x and calculate to obtain the value of x.

Complete step by step solution
It is given that \[0.0\overline {37} \] stands for the number \[0.0373737...\]
Now, suppose that \[x = 0.0373737...\]
Multiply 1000 to both sides of the equation \[x = 0.0373737...\].
So,
\[1000x = 37.3737...\]
Now, multiply 10 to both sides of the equation \[x = 0.0373737...\].
So,
\[10x = 0.373737...\]
Subtract 10x from 1000x to obtain the required value of x.
\[1000x - 10x = 37.3737... - 0.3737...\]
Divide both sides of the equation \[1000x - 10x = 37.3737... - 0.3737...\]
 by 990.
\[990x = 37\]
\[x = \dfrac{{37}}{{990}}\]

The correct option is B.

Additional information In this given problem we are using a trick to obtain the required answer, that trick is first we multiply the number by 1000 then by 10, and subtract them to obtain an integer only. This trick makes the problem easy to solve.

Note Students should know about the place value and face value of a digit in any given number. The place value helps us to know the value of each digit in any number. Without the knowledge of place value and face value, this type of problem can not be solved.