How many two-digit numbers have a tens digit that is greater than the units digit?
units: 0-8
tens: 1-9,2-9,...8-9,9
9+8+7+...+1 = 45
To find the number of two-digit numbers having a tens digit greater than the units digit, we can use a step-by-step approach.
Step 1: Determine the range of possible digits for the tens and units place.
Since we are looking for two-digit numbers, the tens place can have values from 1 to 9 (excluding 0), and the units place can have values from 0 to 9.
Step 2: Count the number of ways to choose the tens and units digits.
The tens digit must be greater than the units digit, so we have a restricted choice for each place value.
For the tens place, we can choose a digit from 2 to 9 (total 8 options).
For the units place, we can select any digit from 0 to 9 (total 10 options).
Step 3: Calculate the total number of two-digit numbers.
Multiply the number of options for each place value:
Total number of two-digit numbers = Number of options for the tens place × Number of options for the units place = 8 × 10 = 80.
Therefore, there are a total of 80 two-digit numbers that have a tens digit greater than the units digit.