The method to represent and work with numbers is understood as a numeration system or number system. A number system may be a system of writing to represent numbers. It’s the notation to represent numbers of a given set by using digits or other symbols. It allows us to work on arithmetic operations like division, multiplication, addition, subtraction.
Some important number systems are as follows:
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
What are Whole Numbers?
The whole numbers are the numbers without fractions, decimals and are a collection of positive integers from 0 to infinity. All the whole numbers exist in number lines. All the entire numbers are real numbers but we will not say that each one of the important numbers is a whole number. Whole numbers cannot be negative. The whole numbers are represented by the symbol “W”. The examples are: 0, 23, 34, 45, 67, 867, 345, 56754, etc.
Properties of Whole Numbers
Properties of whole numbers help us to know the numbers better. Moreover, they create calculations under certain operations like addition, subtraction, multiplication, and division very simple. The different sorts of properties of whole numbers are follows:
- Closure for addition and multiplication.
- Commutative property for addition and multiplication.
- Associative property for addition and multiplication.
- Distributive property of multiplication over addition.
- Identity for addition and multiplication.
Steps to Find whole numbers between numbers:
Following are the steps to find whole numbers between numbers excluding those numbers:
Step 1: Subtract the numbers.
Step 2: Subtract 1 from the result.
For Example: Whole numbers between 10 and 5 are 10-5-1 = 4 i.e. 6, 7, 8, and 9
How many whole numbers are between 20.16 and 3.17?
Since whole numbers do not include fractions and decimal values, 20.16 and 3.17 will not be considered as whole numbers. But, it can be rounded off to the nearest whole number possible.
Therefore the nearest whole number for 20.16 will be 20 and for 3.17 it will be 3, because if the digit after the decimal is less than or equal to 5, the decimal is rounded up to the next whole number.
Now, we have to find the whole numbers between 20 and 3.
- Subtract the numbers
- Subtract 1 from the obtained result.
Therefore, 20 – 3 = 17 and 17 – 1 = 16
Therefore, there are 16 whole numbers between 20 and 3 which are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19.
Sample Problems
Question 1. How many whole numbers are between 15 and 7?
Answer:
Here given two numbers 15 and 7.
- Subtract the numbers
- Subtract 1 from the obtained result.
15 – 7 = 8
8 – 1 = 7
Therefore, there are 7 whole numbers between 15 and 7 are 8, 9, 10, 11, 12, 13, 14.
Question 2. How many whole numbers are between 4.58 and 13.7?
Answer:
Since whole numbers do not include fractions and decimal values, 4.58 and 13.7 will not be considered as whole numbers. But, it can be rounded off to the nearest whole number possible.
Therefore the nearest whole number for 4.58 will be 5 and for 13.7 it will be 14, because if the digit after decimal is greater than or equal to 5, the decimal is rounded up to the next whole number.
Now, we have to find the whole numbers between 14 and 5.
- Subtract the numbers
- Subtract 1 from the obtained result.
14 – 5 = 9
9 – 1 = 8
Therefore, there are 8 whole numbers between 14 and 5 which are 6, 7, 8, 9, 10, 11, 12, 13.
Question 3. How many whole numbers are between 45 and 61?
Answer:
Here given two numbers 45 and 61.
- Subtract the numbers
- Subtract 1 from the obtained result.
61 – 45 = 16
16 – 1 = 15
Therefore, there are 15 whole numbers between 45 and 61 which are 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,57, 58, 59, 60.