these are the problems to convert to base 10.
1. CDXLIV
2. 432 then has five next to it
3. ET0 then has twelve next to it
4. 1011 then has two next to it
5. 4136 then has seven next to it
I do not remember Roman numerals
432 base 5 = 2*5^0 +3*5^1 + 4*5^2 = 2+15+100 =117
A = 10
B = 11
C = 12 in base 12. I can not imagine what E and T are
ET0 base 12 = ?
1011 = 1*2^0 + 1*2^1 + 0*2^2 + 1*2^3
= 1+2+0+8 = 11
4136 base 7 = 6*7^0 + 3*7^1 + 1*7^2 + 4*7^3
= 6+21+49+1372 = 1448
To convert these numbers to base 10, we need to understand the positional value of each digit. In base 10, each digit's positional value is determined by its place in the number, counting from right to left.
1. CDXLIV:
- C represents 100 in Roman numerals.
- D represents 500 in Roman numerals.
- X represents 10 in Roman numerals.
- XL represents 40 in Roman numerals.
- IV represents 4 in Roman numerals.
To convert this to base 10, we add up the positional values: 100 + 500 + 40 + 4 = 644.
2. 432 then has five next to it:
- 432 represents a three-digit base 5 number.
- The leftmost digit has a positional value of 5^2 = 25.
- The middle digit has a positional value of 5^1 = 5.
- The rightmost digit has a positional value of 5^0 = 1.
To convert this to base 10, we multiply each digit by its positional value and add them together: (4 × 25) + (3 × 5) + (2 × 1) = 100 + 15 + 2 = 117.
3. ET0 then has twelve next to it:
- ET0 represents a three-digit base 12 number.
- The leftmost digit (E) has a positional value of 12^2 = 144.
- The middle digit (T) has a positional value of 12^1 = 12.
- The rightmost digit (0) has a positional value of 12^0 = 1.
To convert this to base 10, we multiply each digit by its positional value and add them together: (E × 144) + (T × 12) + (0 × 1).
4. 1011 then has two next to it:
- 10112 represents a four-digit base 2 (binary) number.
- The leftmost digit has a positional value of 2^3 = 8.
- The second-to-left digit has a positional value of 2^2 = 4.
- The second-to-right digit has a positional value of 2^1 = 2.
- The rightmost digit has a positional value of 2^0 = 1.
To convert this to base 10, we multiply each digit by its positional value and add them together: (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 8 + 0 + 2 + 1 = 11.
5. 4136 then has seven next to it:
- 41367 represents a five-digit base 7 number.
- The leftmost digit has a positional value of 7^4 = 2401.
- The second-to-left digit has a positional value of 7^3 = 343.
- The third-to-left digit has a positional value of 7^2 = 49.
- The second-to-right digit has a positional value of 7^1 = 7.
- The rightmost digit has a positional value of 7^0 = 1.
To convert this to base 10, we multiply each digit by its positional value and add them together: (4 × 2401) + (1 × 343) + (3 × 49) + (6 × 7) + (7 × 1).