Convert the following in decimal expression:
A) \[\dfrac{{15}}{{600}}\]
B) \[\dfrac{{23}}{{200}}\]

Hint:
Here we need to convert the given fractions in the decimal form. We will use the long division method and divide the numerator by denominator to get the required number. A decimal number is defined as a number that contains fractional and integer parts but they are separated by a decimal point.

Complete Step by Step Solution:
Here we need to convert the given fractions into decimal form.
A) We can write \[\dfrac{{15}}{{600}}\] as
\[\dfrac{{15}}{{600}} = \dfrac{{15}}{6} \times \dfrac{1}{{100}}\]
Now we can see that there is a common factor between 15 and 6.
So, dividing the numerator and denominator by 3, we get
\[ \Rightarrow \dfrac{{15}}{{600}} = \dfrac{5}{2} \times \dfrac{1}{{100}}\]
 Now dividing 5 by 2, we get
\[ \Rightarrow \dfrac{{15}}{{600}} = 2.5 \times \dfrac{1}{{100}}\]
Now, we know that \[\dfrac{1}{{100}} = 0.01\].
We will substitute this value in the above equation. Therefore, we get
\[ \Rightarrow \dfrac{{15}}{{600}} = 2.5 \times 0.01\]
On multiplying these numbers, we get
\[ \Rightarrow \dfrac{{15}}{{600}} = 0.025\]
Hence, the value of \[\dfrac{{15}}{{600}}\] in decimal form is equal to \[0.025\].

B) We can write \[\dfrac{{23}}{{200}}\] as
\[\dfrac{{23}}{{200}} = \dfrac{{23}}{2} \times \dfrac{1}{{100}}\]
Now dividing 23 by 2, we get
\[ \Rightarrow \dfrac{{23}}{{200}} = 11.5 \times \dfrac{1}{{100}}\]
We know that \[\dfrac{1}{{100}} = 0.01\]
We will substitute this value in the above equation.
\[ \Rightarrow \dfrac{{23}}{{200}} = 11.5 \times 0.01\]
On multiplying these numbers, we get
\[ \Rightarrow \dfrac{{23}}{{200}} = 0.115\]
Hence, the value of \[\dfrac{{23}}{{200}}\] in decimal form is equal to \[0.115\].

Note:
While converting the fraction into decimal using the long division method we need to be aware where we have to put the decimal point. When we get a remainder other than zero and less than the divisor, then we will add 0 to the remainder and decimal point in the quotient. Then we will be able to divide the number again by the divisor. Now if we again get remainder other than zero and less than the divisor, then we will add 0 in the quotient and not the decimal point.