Question

Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively.
a. 144 five
b. 11010 two
c. 53T twelve

Answer 1

any ideas?

Answer 2

do you know how base 10 (our decimal system) works?

Answer 3

no i dont i get confused

Answer 4

so the first spot to the left of the decimal is \(10^0=1\), the next one to the left is \(10^1=10\) and the next to the left is \(10^2=100\), and so on.

so when we write 123 this means \(1\times 10^2+2\times 10^1+3\times 10^0\) which is 100 + 20 + 3

when some number is written in a different base, it follows the same convention. so for example, in base 3 the first spot to the left of the decimal is \(3^0=1\), the next one to the left is \(3^1=3\) and the next to the left is \(3^2=9\), and so on. So a number like 221 in base 3 means \(2\times 3^2+2\times 3^1+1\times 3^0\) which is 18 + 6 + 1= 25.

Answer 5

that is, 25 in base 10.

Answer 6

okay i get it now. thank you

Answer 7

k so did you get the first number?

Answer 8

I think I did

Answer 9

what did you get?

Answer 10

45 if I did it right

Answer 11

not quite, but close. you should be adding 3 numbers together, right? can you tell me ehat they are?

Answer 12

oooops..."what" not "ehat"

Answer 13

well I did 1X5^2+4X5^1+4X5^0

Answer 14

great! \(5^2=25\), \(5^1=5\), \(5^0=1\) so you should get 25 + 20 + 4, right?

Answer 15

yes!

Answer 16

so the total is...

Answer 17

49

Answer 18

yep, there you go!

Answer 19

Thank you!

Answer 20

you're welcome!