find the number of two digit natural numbers such that the tens digit is greater than the units digit.
20 21
30 31 32
...
90 91 92 ... 98
2+3+...+9
= 44
Write in extension the set S of the two digit natural integers whose tens digit is twice that of the unit digit
To find the number of two-digit natural numbers where the tens digit is greater than the units digit, we need to determine the possible values for the tens and units digits.
Since the tens digit should be greater than the units digit, we have the following possibilities for the tens digit: 1, 2, 3, 4, 5, 6, 7, 8, 9.
For each tens digit, we then have the following possibilities for the units digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
However, if the units digit is greater than or equal to the tens digit, it will not satisfy the condition. So, for each tens digit, we need to remove certain units digits.
When the tens digit is 1, there are no units digits that satisfy the condition (1 < 1), so we exclude it.
When the tens digit is 2, the only units digit that satisfies the condition is 1.
When the tens digit is 3, the units digits that satisfies the condition are 1 and 2.
Similarly, when the tens digit is 4, the units digits that satisfy the condition are 1, 2, and 3.
Following this pattern, we find:
For the tens digit 1, there are 0 units digits that satisfy the condition.
For the tens digit 2, there is 1 unit digit that satisfies the condition.
For the tens digit 3, there are 2 unit digits that satisfy the condition.
For the tens digit 4, there are 3 unit digits that satisfy the condition.
Continuing in this manner, we find that:
- For the tens digit 9, there are 8 units digits that satisfy the condition.
In total, we add up the number of units digits for each tens digit:
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
Therefore, there are 36 two-digit natural numbers where the tens digit is greater than the units digit.
To find the number of two-digit natural numbers in which the tens digit is greater than the units digit, we need to follow these steps:
Step 1: Determine the range of values for the tens digit. Since it must be greater than the units digit, the possible values for the tens digit are 1 to 9.
Step 2: Determine the range of values for the units digit. Since it only needs to be a natural number (0 to 9), there are no restrictions on the units digit.
Step 3: Count the number of possible combinations. For each value of the tens digit (1 to 9), there are 10 possible values for the units digit (0 to 9). Therefore, the total number of combinations is 9 (the number of possible tens digits) multiplied by 10 (the number of possible units digits), which equals 90.
So, there are 90 two-digit natural numbers such that the tens digit is greater than the units digit.