Question

The decimal form of $\dfrac{{15}}{{1000}}$ is
A. $15$
B. $150$
C. $0.15$
D. $0.015$

Answer 1

Hint: As we can see in the above question, we have a fraction and we have to convert it to decimal. The fraction given above is called a decimal fraction. We know that any fraction where the denominator i.e. the bottom number is a power of $10$ , is called a decimal fraction. We can write decimal fractions with decimal points and no denominator.We can write it into decimal by placing digits of the numerator to the right of the decimal.

Complete step by step answer:
Let us first define what a fraction and decimal number is:
Fractions: We know that fractions represent a part of a whole. We can write a fraction of any of equal parts. fraction is written as,
$\dfrac{p}{q}$
where “$p$” is the numerator and “$q$” is the denominator of the fraction.

Decimal number: A number that has a decimal value along with its integer value i.e.
$5.4$ , where $5$ is the integer and $4$ is the decimal number. Also the dot between them is called a decimal point i.e. $\left( . \right)$

Here we have been given the fraction:
$\dfrac{{15}}{{1000}}$
We can write the denominator of the fraction as
$\dfrac{{15}}{{{{10}^3}}}$ because we know that $1000 = {10^3}$
So we can see that the denominator has the power $3$.
So we place the decimal point before the three digits in the numerator.
It can be written as
$\dfrac{5}{{1000}} = 0.015$.

Hence the correct option is D.

Note: We should note that there is an alternate way to solve this question also. We can reduce the fraction to the simplest form carrying out all the factors from the numerator and denominator and then we can divide the fraction and write the decimal form. So we can write the factors of the numerator
 $15 = 5 \times 3$
Similarly the factors of the denominator are
$1000 = 10 \times 10 \times 10$
Now we can write the fraction in new form i.e.
$\dfrac{{5 \times 3}}{{10 \times 10 \times 10}}$
The simplest form of the above form is
$\dfrac{3}{{2 \times 10 \times 10}} = \dfrac{3}{{200}}$
Now we can divide the simplest form and write the decimal:
$\dfrac{3}{{200}} = 0.015$
It gives the same answer.