Question

0.0405 divided by 0.9

Answer 1

Consider the given statement,0.

The equivalent mathematical expression will be,

`(0.0405)/(0.9)`

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,

`\begin{gathered} (0.0405)/(0.9) \\ =(0.0405)/(1)*(1)/(0.9) \\ =(00405)/(10000)*(10)/(9) \end{gathered}`

It is known that leading zeroes of a number have no significance. So remove the leading zeroes, and simplify the expression as follows,

`\begin{gathered} =(405)/(10000)*(10)/(9) \\ =(9*45)/(1000*10)*(10)/(9) \\ =(45)/(1000) \end{gathered}`

Now, apply the above steps to convert the fraction to deimal form,

`(0045)/(1000)=0.045`

Thus, the 0.0405 divided by 0.9 gives 0.045