Expressing a repeating decimal in the form of p/q:

To express a repeating decimal in the form of p/q, we need to follow the steps below:

Step 1: Let x be the repeating decimal.
Step 2: Multiply both sides of the equation by 10^n, where n is the number of digits in the repeating part.
Step 3: Subtract x from 10^n x.
Step 4: Solve for x and simplify the answer to the form of p/q.

So, for the given decimal 0.17373..., we can express it in the form of p/q as follows:

Let x = 0.17373...
Multiplying both sides by 100, we get:
100x = 17.3737...

Subtracting x from 100x, we get:
99x = 17.2

Solving for x, we get:
x = 17.2/99

Simplifying the fraction, we get:
x = 172/990

Therefore, the decimal 0.17373... can be expressed in the form of p/q as 172/990.

Introduction to Number System:

The number system is a mathematical system used to represent numbers. It includes different types of numbers such as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and complex numbers. Each type of number has its unique properties and rules for operations.

Natural Numbers: Natural numbers are the counting numbers that start from 1 and go up to infinity. They do not include zero or negative numbers.

Whole Numbers: Whole numbers are the natural numbers along with zero. They do not include negative numbers.

Integers: Integers are the set of whole numbers along with their negative counterparts.

Rational Numbers: Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero.

Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction and have an infinite number of non-repeating decimal places.

Complex Numbers: Complex numbers are numbers that contain a real part and an imaginary part, represented as a+bi, where a and b are real numbers and i is the imaginary unit.

In conclusion, understanding the number system is essential in mathematics as it allows us to perform mathematical operations and solve problems using the appropriate type of numbers.

If the bar is on 73 then we need to take 1 before decimal so that after decimal every number has bar. And it can be called Equation 1.
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let x = 0.173

to take 1 to before decimal we need to multiply x with 10.
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10x = 1.73 -----Equation 1
now we need to take 73 before decimal so we need to multiply 10x*100
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1000 x = 173.73 -----Equation 2
we have taken one 73 before decimal but still there are many 73. that's why there is still 73 bar in equation two.
Now subtract equation 1 from equation 2
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1000x = 173.73
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- 10x = 001.73
900x = 172.00

x = 172/900