Question 1: Why can we not divide by 0?

Division is defined as the inverse operation of multiplication. For any two numbers A and B, dividing A by B means finding a number C such that when multiplied by B, it gives A. Formally, division is expressed as: AB=C ifandonlyif BC=A

However, when B=0, this definition breaks down. Suppose we try to compute A0=C This implies 0C=A

But 0C=0 for any value of C, so there is no number C that satisfies the equation unless A=0 =. This means division by zero is undefined because it violates the fundamental property of division as the inverse of multiplication.

Additionally, division by zero leads to contradictions and breaks the consistency of arithmetic rules. Therefore, dividing by zero is undefined and not allowed in mathematics.

Question 2: Why is the Hindu-Arabic numeral system better than the Roman numeral system? What is place value?

The Hindu-Arabic numeral system is superior to the Roman numeral system primarily because it includes the concept of place value and the digit zero, which allow for efficient representation and calculation.

Place value is the principle that the value of a digit depends on its position in a number. For example, in the number 345:

• The digit 3 is in the hundredth place, representing 300.
• The digit 4 is in the tens place, representing 40.
• The digit 5 is in the unit's place, representing 5.

This positional system enables the expression of large numbers compactly and facilitates arithmetic operations such as addition, subtraction, multiplication, and division.

In contrast, the Roman numeral system uses symbols like I, V, X, L, C, D, and M, without a place value or a zero. This makes Roman numerals cumbersome for arithmetic and limited in expressing large numbers efficiently.

Therefore, the Hindu-Arabic system's place value and zero digit make it a more versatile and practical numeral system for mathematics.

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