How many numbers are there between 1 and 1,000 both inclusive?

Number system, as the name suggests is a system pertaining to numbers in mathematics, which is employed in order to represent numerals using different symbols and variables. The numbers, which are capable of being plotted on a number line, also called real numbers, are represented using a set of values or quantities under the number system. Different types of numbers are categorized into different sets or groups, based upon their varying characteristics. For example, all such numbers which can be written in the form of p/q, where q is a non-zero integer, are called rational numbers. Various types of systems:

• Decimal Number System
• Binary Number System
• Octal Number System
• Hexadecimal Number System

Numbers

Numbers are defined as quantities on which various mathematical operators, such as addition, subtraction, multiplication, and division can be applied. Not only are numbers used in mathematical practice but they also play a crucial role in our daily lives. The fields of accounting, economics, finance, stock markets, marketing, etc. also use numbers as their primary tool for analysis and interpretation.

Based on their properties, numbers are classified as:

• Real Numbers
• Whole Numbers
• Natural Numbers
• Integers
• Rational Numbers
• Irrational Numbers
• Fractions
• Decimal Numbers
• Imaginary Numbers
• Complex Numbers

Whole Numbers

The set of whole numbers includes the entire set of natural numbers as well as the numeral zero. The set of natural numbers is 1, 2, 3, 4, 5, 6, ….; so 0, 1, 2, 3, 4, 5, 6, ….. is the set of whole numbers. Since natural numbers are also referred to as the set of counting numbers, it can be safely stated that whole numbers are the summation of the numeral 0 and the set of counting numbers.

Set of Whole Numbers = 0 + Set of Natural Numbers

How many numbers are there between 1 and 1,000 both inclusive?

Solution:

The number of whole numbers present between two given whole numbers, the extremes inclusive is given by the following formula:

Y – X + 1

where Y refers to the greater of the two numbers, X is the smaller number. And 1 is added at the last to include one of the end points, as both the extremes are to be included in the count as well. As per the question, there are two numbers 1 and 1000, and the number of whole numbers between them, including both can be determined using the following formula Y – X + 1.

Given:

Y = 1000 and X = 1

Now, Y – X = 1000 – 1

= 999

Then, Y – X + 1 = 999 + 1

= 1000

Thus, there are 1000 numbers between 1 and 1000, both inclusive.

Similar Problems

Question 1. How many whole numbers are there between 0 and 100; both inclusive?

Solution:

Given:

Y = 100 and X = 0

Now,  Y – X = 100 – 0

= 100

Then, Y – X + 1 = 100 + 1

= 101

Thus, there are 101 whole numbers between 0 and 100, both inclusive.

Question 2. How many whole numbers are there between 69 and 420; both inclusive?

Solution:

Given:

Y = 420 and X = 69

Now,  Y – X = 420 – 69

= 351

Then, Y – X + 1 = 351 + 1

= 352

Thus, there are 352 whole numbers between 69 and 420, both inclusive.

Question 3. How many whole numbers are there between 1 and 69; both inclusive?

Solution:

Given:

Y = 69 and X = 1

Now,  Y – X = 69 – 1

= 68

Then, Y – X + 1 = 68 + 1

= 69

Thus, there are 69 whole numbers between 1 and 69, both inclusive.

Question 4. How many whole numbers are there between 1,000 and 1,00,000; both inclusive?

Solution:

Given:

Y = 1,00,000 and X = 1,000

Now,  Y – X = 1,00,000 – 1,000

= 99,000

Then, Y – X + 1 = 99,000 + 1

= 99,001

Thus, there are 99,001 whole numbers between 1,000 and 1,00,000, both inclusive.

Question 5. How many whole numbers are there between 3 and 500; both inclusive?

Solution:

Given:

Y = 500 and X = 3

Now,  Y – X = 500 – 3

= 497

Then, Y – X + 1 = 497 + 1

= 498

Thus, there are 498 whole numbers between 3 and 500, both inclusive.