Write the base-ten representation for each of the following base-five numerals.
a) 413five
b) 2001five
c) 31five
your turn ...
To convert base-five numerals to base-ten representation, you need to multiply each digit by the corresponding power of 5 and then sum up the results.
a) 413five:
To convert this number to base ten, you need to evaluate:
4 * 5^2 + 1 * 5^1 + 3 * 5^0
Calculations:
4 * 25 + 1 * 5 + 3 * 1 = 100 + 5 + 3 = 108
Therefore, the base-ten representation of 413five is 108.
b) 2001five:
To convert this number to base ten, you need to evaluate:
2 * 5^3 + 0 * 5^2 + 0 * 5^1 + 1 * 5^0
Calculations:
2 * 125 + 0 * 25 + 0 * 5 + 1 * 1 = 250 + 0 + 0 + 1 = 251
Therefore, the base-ten representation of 2001five is 251.
c) 31five:
To convert this number to base ten, you need to evaluate:
3 * 5^1 + 1 * 5^0
Calculations:
3 * 5 + 1 * 1 = 15 + 1 = 16
Therefore, the base-ten representation of 31five is 16.
a) To convert the base-five numeral 413five to base-ten, we can use the following calculation:
4 * 5^2 + 1 * 5^1 + 3 * 5^0
= 4 * 25 + 1 * 5 + 3 * 1
= 100 + 5 + 3
= 108
Therefore, the base-ten representation of 413five is 108.
b) To convert the base-five numeral 2001five to base-ten, we can use the following calculation:
2 * 5^3 + 0 * 5^2 + 0 * 5^1 + 1 * 5^0
= 2 * 125 + 0 * 25 + 0 * 5 + 1 * 1
= 250 + 0 + 0 + 1
= 251
Therefore, the base-ten representation of 2001five is 251.
c) To convert the base-five numeral 31five to base-ten, we can use the following calculation:
3 * 5^1 + 1 * 5^0
= 3 * 5 + 1 * 1
= 15 + 1
= 16
Therefore, the base-ten representation of 31five is 16.