convert the numeral to a numeral in base 10
43
5
represent 555 in base 5
To convert a numeral in a base other than 10 to a numeral in base 10, you need to multiply each digit of the number by the corresponding power of the base and then add them together.
For example, to convert the numeral 43 in base 5 to base 10:
1. Split the numeral into its individual digits: 4 and 3.
2. Multiply each digit by the corresponding power of the base. In this case, we start from the rightmost digit and assign powers of 5 to each digit from right to left. So, the rightmost digit "3" is multiplied by 5^0 (which is 1) and the leftmost digit "4" is multiplied by 5^1 (which is 5).
- 3 * 5^0 = 3 * 1 = 3
- 4 * 5^1 = 4 * 5 = 20
3. Add the results together: 3 + 20 = 23.
Therefore, the numeral 43 in base 5 is equal to 23 in base 10.
Do you mean to convert 435 to base 10?
In base 10, we have the right most digit to represent 0 to 9, the second (from right) to represent 10 (=10²), the rhidr to represent 100 (=10³)and so on.
The same goes with base 5, the right-most digit stands for 0 to 4 (1 less than 5), and the second digit for 5, the third for 5²=25, etc.
So 435 = 4*5+3 = 2310.
Notice that students in North America should be able to do interconversion between bases 5 and 10 without difficulties, thanks to the money system.
Consider base 5 as:
1 (1 cent)
5 (1 5-cents, or nickel)
25 (1 25-cents, or quarter).
435 would be equivalent to 4 nickels and 3 cents, which make 23 cents.
Conversely, to convert from base 10 to base 5, we simply express the amount (up to $1.04) in cents, nickels and quarters. For example,
7910
=79 cents
=3 quarters and 4 cents
=3045