Computation of Whole Numbers

The whole number is a subpart of the Number System. Whole numbers are a collection of positive integers plus zero, excluding fractions and decimal numbers, so numbers like 1.503, 8/3, and so on are not whole Numbers. The alphabet ‘W’ provides a symbolic representation of whole numbers. Whole numbers begin with the digit 0 and go to infinity.

The difference between the whole numbers and the natural numbers is that the whole numbers contain zero, whereas the natural numbers exclude zero and start from one.   

Whole numbers are beneficial in the field where one needs mathematical computations. In data science, the numeric ranges generally start from zero, in various data structures where the indexing starts from zero, etc.

The Concept of the Whole Number: 

• As the name implies, a whole number is not a fraction or a decimal, so fractions are not included in whole numbers. And because of this, the whole number is not a fraction, so it cannot be negative

• Whole Numbers is another term for counting numbers 

• The set of Whole Numbers is denoted by the numbers 0 through 1, 2, 3, and so on in mathematics

• According to the facts stated above, natural numbers are a part of whole Numbers, and all whole Numbers are part of counting numbers. The union of all positive counting integers plus zero can also be a whole number

• We can say that zero (0) is the smallest whole number because they begin with zero (0)

• The concept of zero was put by the Indian Mathematician Bramha Gupta 

• Zero is the number between the positive integer number line and the negative integer number line in general terms

Whole Numbers on the Number Line

The following diagram depicts the set of natural numbers and whole numbers:

Properties of the Whole Number

1. Closure Property

The product and the sum of two Whole Numbers always result in a Whole Number. For example, 2 + 10 = 12 (A Whole Number), 2 * 10 = 20( A Whole Number) 

2. Associative Property

Even if the numbers are arranged in a different sequence, the sum or product of the Whole Numbers remains the same.For example, 2 * 10 = 20 and 10 * 2 = 20  , 2 + 10 = 12 and 10 + 2 = 12, etc.

3. Additive Identity

If zero is added to any whole number, then the number remains unchanged. It is also one of the Identity properties of the Whole Numbers.

4. Multiplicative Identity

If one is multiplied by any whole number, the whole number remains unchanged. It is also one of the Identity properties of whole numbers.

5. Distributive Property

Solve the outside bracket first and distribute it to the inner elements. The distributive property is the distribution of the expression, and the product remains the same.

For example, ( 10 × 20 ) + ( 10 × 7 ) = 200 + 70 = 270

6. Zero is the only Whole Number that isn’t a Natural Number (0).

7. Fractions and negative numbers are not whole numbers unless and until defined in terms of integers.

Rounding the Fractions, Decimal Numbers to the Nearest Whole Number

Finding the nearest whole value, often known as rounding off a fraction to the nearest whole number, determines which number is closest to a given fraction or decimal number.

• The closest whole number to 4.2, for example, is 4

If the decimal number after the decimal point is less than 0.5, we will throw the integer below that number in the output, which will also be the whole number. 

And, if the decimal number after the decimal point is more significant than 0.5, then the number is appended with one value. 

• If the number is 8.9, then the nearest whole number to 8.9 is 9, and not 8

Conclusion

Thus in this article, we have learned how to compute whole numbers. We have also seen the difference between natural numbers and whole numbers and their various properties. We also saw some computational fields with the application of whole numbers.