Number & Operations for Teachers 

    Copyright David & Cynthia Thomas, 2009

Exercises

 

1.      Complete the following figure and write a question illustrating each of the six indicated connections

 

1.      Complete the following figure and write a question illustrating each of the six indicated connections

 

2.      Complete the following figure and write a question illustrating each of the six indicated connections

 

3.      Fill in the following table as indicated:

Base Ten Number

Base Ten

Model

Base Five Number

Base Five

Model

 

 

 

132

1012five

  45

 

 

 

555

 

 

 

 

 

  134five

 

 

  400five

 

 

 

1020five

 

 

4.      Which number is larger? Explain.

§   1041five or 1101five

§   4234five or 10000five

§   1011two or 1101two

§   10110001two or 10011001two

 

 

5.      Which number is larger?

§   24five or 20 eight

§   101 two or 4 five

§   201 five or 36 ten

 

6.      Given any two whole numbers, one in base five and the other in base ten, how would you decide which is larger?

 

7.      In base ten, multiplying the number 7 by ten produces the number 70.  Multiplying 70 by ten produces the number 700.  Some people generalize observations of this sort by saying “When you multiply any whole number by ten, just add a zero to the right side of the number.” 

§   Does this “rule” always work, or are there conditions that must be met?

§   Why does it work at all? 

§   Make up a similar rule for multiplication in base five and explain why it works.

 

8.      Calculators and computers represent numbers internally using only two numerals, 0 and 1.  Electronically, these numerals correspond to a switch being in the OFF position or the ON position.  Describe a numeration system with only two numerals and explain how you would represent the base ten number 9 using only 0’s and 1’s.

 

9.      Many computer images are composed of picture elements, or pixels, arranged in rectangular arrays.  The color of each pixel is represented in the computer as a binary number having eight places, also known as an 8-bit binary number.  The number of possible colors for any given pixel is the same as the number of possible 8-bit binary numbers.  Using this scheme,

§   How many colors are possible? 

§   How many colors could you get with a 16-bit binary system? 

§   A 24-bit system?