Question

How do you express \[0.6\% \] as a decimal and fraction?

Answer 1

Hint: This is the given number in percentage form. As we need to convert them into decimal and fraction, we will write it in the fraction form first by writing per cent as per 100 and then in decimal form. Then finding the decimal form means putting decimal to that many places to leave as many zeros in the denominator.

Complete step by step solution:
First given that,
 \[0.6\% \] is the given number.
I.Conversion in fraction form:
 \[0.6\% = \dfrac{{0.6}}{{100}}\]
Multiply numerator and denominator by 10
 \[0.6\% = \dfrac{{0.6 \times 10}}{{100 \times 10}} = \dfrac{6}{{1000}}\]
Now we have to simplify the fraction. But in order to simplify this we will find the HCF of both numerator and denominator.
Factors of 6 are \[1,2,3,6\]
Factors of 1000 are \[1,2,5,10,20,50,100,200,500,1000\]
Now we can select here 2 as the highest common factor because no other factor is common except 1 and 2. So dividing both by 2 we get,
 \[0.6\% = \dfrac{3}{{500}}\]
This is a simplified form of fraction for the percentage given.
So, the correct answer is “$\dfrac{3}{{500}}$”.

II.Conversion in decimal form:
We know that,
 \[0.6\% = \dfrac{{0.6}}{{100}}\]
So just shift the decimal to the left of the number such that the number of places to be shifted is equal to zeros in the denominator.
So we can write
 \[0.6\% = 0.006\]
So, the correct answer is “0.006”.

Note: Note that in multiple choice questions sometimes simplified form of fraction is not given then just take the original fraction as an answer.
Decimal is just a sign like a dot. But note that if decimal is not seen in a number it is always at the extreme right end of the number. Here in this case decimal is already present so just shift it.