How many three digit whole numbers are there between 75 and 405?
305
Understanding Three-Digit Whole Numbers
The question asks us to find the count of three-digit whole numbers that fall between 75 and 405. First, let's clarify what three-digit whole numbers are and what it means to be "between" two numbers.
- Whole Numbers: These are non-negative integers (0, 1, 2, 3, ...).
- Three-Digit Numbers: These are whole numbers that have exactly three digits. The smallest three-digit number is 100, and the largest is 999.
So, the set of all three-digit whole numbers is {100, 101, 102, ..., 998, 999}.
Finding Numbers Between 75 and 405
The phrase "between 75 and 405" means the numbers must be strictly greater than 75 and strictly less than 405. We are looking for three-digit whole numbers that satisfy this condition.
- Is 75 a three-digit number? No, it has two digits.
- Is 405 a three-digit number? Yes, but the numbers must be *less than* 405.
We need to find the three-digit numbers that are greater than 75 and less than 405.
Identifying the Range of Numbers
The three-digit numbers start from 100. Since 100 is greater than 75, our range starts at 100.
The numbers must be less than 405. The three-digit numbers just below 405 are 404, 403, and so on. The number 404 is a three-digit number and is less than 405. The number 405 is not included because the range is strictly *between* 75 and 405.
So, the three-digit whole numbers we are interested in are those from 100 up to 404, inclusive. This sequence is 100, 101, 102, ..., 403, 404.
Counting the Numbers in the Range
To count the number of whole numbers in a continuous range from a starting number (first) to an ending number (last), we can use the formula:
Number of terms = Last number - First number + 1
In our case:
- First number = 100
- Last number = 404
Using the formula, the count is:
\( \text{Count} = 404 - 100 + 1 \)
\( \text{Count} = 304 + 1 \)
\( \text{Count} = 305 \)
Therefore, there are 305 three-digit whole numbers between 75 and 405.
Final Answer Calculation
The three-digit whole numbers between 75 and 405 are the numbers in the set {100, 101, ..., 404}.
To find the count, we subtract the smallest number from the largest number in the set and add 1.
\( \text{Total Count} = 404 - 100 + 1 = 305 \)
The number of such numbers is 305.
Revision Table: Key Concepts
| Concept | Description | Example |
|---|---|---|
| Whole Numbers | Non-negative integers (0, 1, 2, ...) | 0, 10, 150, 400 |
| Three-Digit Number | A whole number with exactly three digits | 100, 567, 999 |
| Numbers Between A and B | Numbers > A and < B (A and B are not included) | Numbers between 5 and 10 are 6, 7, 8, 9 |
| Counting Numbers in a Range (inclusive) | Last number - First number + 1 | Count of numbers from 10 to 15 is 15 - 10 + 1 = 6 (10, 11, 12, 13, 14, 15) |
Additional Information: Number Systems
Understanding different types of numbers is fundamental in mathematics.
- Natural Numbers: These are the positive integers starting from 1 (1, 2, 3, ...). Also called counting numbers.
- Whole Numbers: Natural numbers including zero (0, 1, 2, 3, ...).
- Integers: Whole numbers and their negative counterparts (...-3, -2, -1, 0, 1, 2, 3...).
- Rational Numbers: Numbers that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- Irrational Numbers: Numbers that cannot be expressed as a simple fraction, like \( \sqrt{2} \) or \( \pi \).
- Real Numbers: All rational and irrational numbers.
In this problem, we specifically dealt with whole numbers that meet a digit count and range criteria.
Similar Questions
The weights of 3 boxes are 4, 7 and 10 kilograms. Which of the following CANNOT be the total weight, in kilograms, of any combination of these boxes?
The difference between the place values of ‘4’ and ‘2’ in the number 833749502 is:
\(\frac{1}{{300}}\) written as a recurring decimal is:
A fraction when added to 7/3 gives 4. What is the fraction?
Tapas, Avi and Rishi shared a cake. Tapas had 1/2 of it, Rishi had 1/3 of it and Avi had the rest. What was Avi’s share of the cake?
Which of the following is not a triangular number?
Which of the numbers given below is the square root of 15376?
Find a two digit number which is exactly three times the product of its digits.
When 472 pieces of plywood, each 0.23 cm thick, are piled on top of each other, what would be the height of the pile in metre?
If 2/3rd of a pizza costs Rs. 300, then 3/5th of a pizza will cost:
Important Questions from Integers
Find the number of integers between $1$ and $150$ (inclusive) having $7$ as one of the digits but which are not divisible by $7$.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2 The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements:
1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
