In the following decimal,how many 2's are there in all before the hundredth 3?
0.23223222322223
the nth group of digits has n 2's and 1 3
1+2+...+100 = 100(101)/2 = 5050 2's
To determine the number of 2's before the hundredth 3, we need to count the number of digit 2 occurrences before the third decimal place.
Step 1: Count the number of 2's before the hundredth 3.
Starting from the decimal point and moving towards the left, let's count the occurrences of the digit 2 until we reach the hundredth 3.
0.23223222322223
First, we have a 2 before the decimal point.
Next, counting the digits after the decimal point:
- The first digit after the decimal point is not a 2.
- The second digit after the decimal point is a 2.
- The third digit after the decimal point is a 2.
- The fourth digit after the decimal point is a 2.
Thus, there are 4 occurrences of the digit 2 before the hundredth 3.
To find the number of 2's before the hundredth 3 in the given decimal, you need to examine the digits one by one until you reach the hundredth 3.
Starting from the leftmost digit, you can keep a count of the number of 2's encountered until you reach the hundredth 3. Here's a step-by-step breakdown:
1. Look at the first digit after the decimal point, which is 2. Increment the count of 2's encountered by 1.
Count: 1
2. Move to the next digit, still a 2. Increment the count by 1.
Count: 2
3. Continue moving to the right and counting the 2's:
- Next digit: 3 (stop counting, as this is the hundredth 3)
By following this process, you can see that there are 2 occurrences of 2 before the hundredth 3 in the given decimal.