Question

Simplify the following $ \dfrac{{0.009}}{?} = 0.01 $
A. 0.0009
B. 0.09
C.0.9
D. 9

Answer 1

Hint: Since the question involves decimals therefore we must know that the decimals can be converted into fractions and vice versa. Decimal numbers can be expanded in three ways which are-place value form, decimal form and fractional form.

Complete step-by-step answer:
Now let us understand the concept of converting a decimal number into a fraction, to do so one needs to write the given decimal number as the numerator with no decimal point and in the denominator, write 1 followed by as many zeros as there are digits after the decimal in the given number .therefore the above question can be written as
 $
  \dfrac{{0.009}}{?} = 0.01 \\
\Rightarrow \dfrac{{0.009}}{x} = 0.01 \;
 $
Let us suppose the number to be calculated be x, then let us try to eliminate the denominator which can be done by multiplying the equation with ‘x’ on both the sides in this case.
 $ \Rightarrow x \times \dfrac{{0.009}}{x} = x \times 0.01 $
Simplifying we will cancel the terms and reorder the equation so that we can get all the constants at one place and then calculate value of ‘x’
 $ \dfrac{{0.009}}{{0.01}} = x $
Now we will be converting the decimals into fraction by the method explained above. Therefore we get
 $ \dfrac{9}{{1000}} \times \dfrac{{100}}{1} = x $
We observe that 0.009 has three decimal places that is 1 followed by three zeros and 0.01 has two decimal places that is 1 followed by two zeros. Now to eliminate the fraction denominator we will cancel the terms that are the zeros from numerator and denominator which gives us
 $ \dfrac{9}{{10}} = x $
Since we have the options as decimal we will convert the fraction into decimal and hence the value of x will be:
0.9=x
So, the correct answer is “Option C”.

Note: We must understand that decimals are fractions with denominators 10, 100, 1000, and higher multiples of 10. To convert these fractions into decimals, look at the denominator. There should be as many digits after the decimal point as there are zeros in the denominator. Each place to the right of the decimal point is a decimal place.