convert from decimal to the indicated base. 56 to base 5. i know theres long division involved but i have no idea what to do after. i did 5\56 & got 11 then 5/11 & got 2 & then 5/2 to finally get a remainder of 0 what do i do now!?
break it down to multiples of 5
56 = 2(5^2) + 1(5) + 1
= 2115
here is a great calculator for checking
enter 56 in the base 10 box
http://www.cleavebooks.co.uk/scol/calnumba.htm
how did you get 2115?
Ummmh, it's not 2115 , it's 211 base 5
as you requested
I laid it out for you
56 = 2(5^2) + 1(5) + 1
so 2 1 1 (base 5)
To convert from decimal to another base, such as base 5 in this case, you can follow these steps:
1. Divide the decimal number by the base (in this case, 5).
2. Write down the remainder from the division in the rightmost position.
3. Divide the quotient from the previous step (excluding any remainder) by the base again.
4. Repeat steps 2 and 3 until the quotient is zero.
5. Write the remainders in reverse order from right to left to obtain the converted number.
Let's work through the example of converting 56 to base 5:
1. Divide 56 by 5: 56 ÷ 5 = 11 with a remainder of 1 (write down the remainder at the rightmost position).
2. Divide 11 by 5: 11 ÷ 5 = 2 with a remainder of 1 (write down the remainder after the previous one).
3. Divide 2 by 5: 2 ÷ 5 = 0 with a remainder of 2 (write down the remainder).
4. Since the quotient is now zero, we stop the division.
5. Finally, write the remainders in reverse order: The remainders are 2, 1, 1, so the converted number is 211 in base 5.
Therefore, 56 in decimal is equal to 211 in base 5.