what are the place values in a base b place-value system? What digits are needed?

Question

I'm not really sure what this question is even asking.

Answer 1

The digits are 0,1,2,3,...,b-1

 

The base place value is b^0 = 1

The next largest place value is b^2.

The next after that is is b^3.

etc etc

The next smallest place value is b^(-1) = 1/b

The next smallest place value after that is b^(-2) = 1/(b^2)

THe next after that is b^(-3) = 1/(b^3)

 

EXAMPLE:  BASE 10

 

THe digits are 0,1,2,3,4,5,6,7,8,9

 

The base place value is 10^0 = 1.

The next largest place value after that is 10^1 = 10

THe next largest place value after that is 10^2 = 100

THen 10^3 = 1000, then 10^4 = 10000 etc etc etc

The next smallest place value before that is 10^(-1) = 1/10 = 0.1

THe next smallest place value before that is 10^(-2) = 1/(10^2) = 1/100 = 0.01

Then after that 1/10^3 = 10^(-3) = 1/1000 = 0.001

etc etc etc

 

 

EXAMPLE: Base 2

 

THe digits are 0,1

 

Place values: 

  base place value is 2^0 = 1

 next one after that is 2^1 = 2

  next one after that is 2^2 = 4

 then 2^3 = 8, 2^4 = 16, etc etc etc

 place value smaller than 1:  2^(-1) = 1/2 , 2^(-2) = 1/2^2 = 1/4 , 1/2^3 = 1/8. 1/2^4 = 1/16, etc etc etc

 

Do you understand?