Question

Express the following decimal in the form \[\dfrac{p}{q}:0.47\]
a) \[\dfrac{{43}}{{90}}\]
b) \[\dfrac{{43}}{9}\]
c) \[\dfrac{{43}}{{900}}\]
d) None of the above

Answer 1

Hint: In this we need to convert \[0.47\] into the \[\dfrac{p}{q}\] form. \[0.47\] is a terminating decimal number i.e. it has finite numbers after a decimal point. Now, to convert these types of numbers in decimal form, we remove the decimal point and divide it with \[1\] followed by an equal number of zeroes as the number of digits after the decimal point.

Complete step-by-step solution:
We need to convert \[0.47\].
We see that there are \[2\] digits after the decimal point. So, we need to divide the given number by \[1\] followed by \[2\] zeroes i.e. we remove the decimal point from the given number and divide it by \[100\].
\[0.47\] can be represented as \[\dfrac{{047}}{{100}}\].
We know, zeroes in the starting of a number makes no sense. So, we can write \[\dfrac{{047}}{{100}}\] as \[\dfrac{{47}}{{100}}\].
As this fraction cannot be simplified further, this is our required answer.
\[0.47\] in \[\dfrac{p}{q}\] from is \[\dfrac{{47}}{{100}}\].
When we see the option given, we see no option equal to \[\dfrac{{47}}{{100}}\]. But, we can choose “None of the above” option as option a), b) and c) are not the required answers.
Therefore, the correct option is (d).

Note: While converting the decimal numbers in \[\dfrac{p}{q}\], we need to check the number of digits after the decimal point. After dividing the given number by the number of zeroes required, we see if we can further simplify or not. If we can further simplify, we need to simplify otherwise we can leave it as it is.