<h3>Complete Question</h3>
Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?
The possible values of b are 4 and 5
<h3>How to determine the possible numbers of b?</h3>
The conditions are given as:
- b is at least 2
- When 197 in base b has 4 digits.
So, we start by converting 197 to base 2 and above.
This is done as follows:
<u>197 to base 2</u>
2 | 197
98 R 1
49 R 0
24 R 1
12 R 0
6 R 0
3 R 0
1 R 1
0 R 1
So, we have:
197 = 11000101 in base 2
11000101 has more than 4 digits.
This means that b cannot be 2
Using the above method of conversion, we have:
- 197 = 21022 in base 3
- 197 = 3011 in base 4
- 197 = 1242 in base 5
- 197 = 525 in base 6
- 197 = 401 in base 7
See that as the base increases, the number of digits decreases.
The numbers in base 4 and 5 have 4 digits.
Hence, the possible values of b are 4 and 5
Read more about base conversions at:
brainly.com/question/17946394
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