Respuesta :
Consider the given statement,0.
The equivalent mathematical expression will be,
[tex]\frac{0.0405}{0.9}[/tex]Consider that a decimal number can be converted into a fraction using the following steps;
i) Identify the number of digits after the decimal in the number. Suppose there are 'x' digits after decimal.
ii) Then remove the decimal and put a 1 in the denominator, and then put as many zeroes as there were number of digits after the decimal i.e. x .
Now, apply this algorithm to the expression,
[tex]\begin{gathered} \frac{0.0405}{0.9} \\ =\frac{0.0405}{1}\times\frac{1}{0.9} \\ =\frac{00405}{10000}\times\frac{10}{9} \end{gathered}[/tex]It is known that leading zeroes of a number have no significance. So remove the leading zeroes, and simplify the expression as follows,
[tex]\begin{gathered} =\frac{405}{10000}\times\frac{10}{9} \\ =\frac{9\times45}{1000\times10}\times\frac{10}{9} \\ =\frac{45}{1000} \end{gathered}[/tex]Now, apply the above steps to convert the fraction to deimal form,
[tex]\frac{0045}{1000}=0.045[/tex]Thus, the 0.0405 divided by 0.9 gives 0.045
