convert the numeral to a numeral in base 10
14
5
The "1" stands for 5 in base 5.
145
=(1*5)+4
=?
4.5 + 1.1
20 + 1
21
Your working is for
415
=4.5 + 1.1
=20 + 1
=21
The units digit is multiplied by 1, and the second digit from the right is multiplied by the base, 5 in this case.
If the number has more than 2 digits, the next digits (to the left) are multiplied by the subsequent powers of the base.
Example:
3217
=3*7^2 + 2*7^1 + 1*7^0
=3*49 + 2*7 + 1*1
=147 + 14 + 1
=162
So
415
=4*5^1 + 1*5^0
=4*5 + 1*1
=21
To convert a numeral in a different base to base 10, you need to follow these steps:
1. Identify the base of the given numeral: In this case, the numeral is "14" with no additional information. By default, we assume it is in base 10.
2. Write down the digits of the numeral: The numeral "14" has two digits, 1 and 4.
3. Calculate the value of each digit: Since the base is 10, each digit holds its face value. The digit 1 is in the ones place, so it represents 1. The digit 4 is in the tens place, so it represents 4 * 10 = 40.
4. Add up the values of all the digits: Add the values calculated in the previous step. In this case, 1 + 40 equals 41.
So, the numeral "14" in base 10 is equal to 41.