## Esmy 3 years ago while i type it down Add in the indicated base.

1. Esmy

|dw:1348275214866:dw|

2. Esmy

|dw:1348275306258:dw|

3. muffin990

do you go to James Madison High School

4. oldrin.bataku

What base does it want you to add in?

5. Esmy

I'm not sure thats how it says :/

6. Esmy

No I go to Hanna High

7. muffin990

I was just wondering i go to James Madison and I had this question on one of my exams but I could not figure out how to do it

8. Esmy

yeah this is hard :/ but I think I got the answer. I'm just checking if I'm correct or not ...

9. muffin990

but i think it was to base 10 if that helps

10. oldrin.bataku

There isn't enough information here. What base? You need to explain. Did you mean this?$44_5+11_5$If so, the correct answer is...$100_5$

11. Esmy

12. Esmy

All the fives are tiny under fives they seem big here, but I think its A. 131$_{5}$

13. oldrin.bataku

Oops, it's C.$44_5+11_5=110_5$

14. muffin990

can you explain how to do it for us since I am having a hard time with it to

15. Callisto

$44_5+11_5$$=(4 \times 5+4\times 5^0) + (1 \times 5^1 + 1\times 5^0)$$=30_{10}$$=1\times 5^2 + 1\times 5^1 + 0\times 5^0$$=110_5$

16. Callisto

Or you can do it in this way: When every time you see 5, you write it as 0, and add one to the next digit, like what you do for 11+9 in base 10. |dw:1348277837985:dw|

17. oldrin.bataku

The subscript here indicates the base, also known as the radix. Typically, we deal with radix ten, or decimal, tied to an Arabic numeral system -- which is why we have ten digits. This developed because humans have ten fingers (or, as they're called in anatomy, digits ;-), so it was natural to base around.$0, 1, 2, 3, 4, 5, 6, 7, 8, 9$Past civilizations have used other choices for their radix and numeral system; in ancient Babylon, the sexagecimal system, which uses radix sixty, was used, with numerals for each. This is why we often speak of multiples of three and six, in things like sixty seconds per minute, sixty minute per hour, sixty arcseconds per arcminute, sixty arcminutes per degree, three-hundred-sixty degrees per circle... the list goes on and on. Anyways, the key here is that different bases use different numerals. For convenience, we reuse our Arabic numeral system for bases that are less than ten. This is why binary, which is often talked about when speaking of electronics and computers, which uses radix two, employs 0, 1 as its numerals -- they are the possible values of an individual bit, or binary digit. Since binary is not easy to deal with, often people use hexadecimal, using radix sixteen, to represent values. They make use of the first six letters of the alphabet to supplement the ten we use, coming up with 0 to 9, followed by A to F. Below are examples of how to interpret numbers in different bases.$173_{10}=1\times10^2+7\times10^1+3\times10^0=100+70+3=173\\FE_{16}=15\times16^1+14\times16^0=15=240+14=254\\1011_2=1\times2^3+0\times2^2+1\times2^1+1\times2^0=8+2+1=11$Note that the term base might remind you of exponentiation and logarithms. That is, it's what is being taken the power of -- just like what is being done here. Now, the actual relevant stuff is easy. Adding in foreign bases is just like you'd normally add, only you have to keep in mind that there is a different number of numerals, so explicit care must be taken to make sure you properly carry.$44_5+11_5$The first thing we do is add the last digits of both.$\ \ \ 1+4=5\\\text{however we are in base 5, so...}\\\ \ \ 1_5+4_5=10_5\\\text{which means we need to carry.}$Now, lets try to add the next digit, making sure to remember the digit carried over.$10_5+10_5+40_5=110_5$Again, we have a digit to carry over, so our result is ultimately...$100_5+10_5+0_5=110_5$Now, to check, let's rewrite them all in decimal and add quickly.$44_5=4\times5^1+4\times5^0=24\\11_5=1\times5^1+1\times5^0=6\\44_5+11_5=24+6=30$$110_5=1\times5^2+1\times5^1+0\times5^0=25+5+0=30$So, it all checks out :-)

18. muffin990

Thank you so much