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 Mathematics Magazine for Grades 1-12  

11/2003

To talk goodness is not good...Only to do it is.
 - Chinese Proverb

Grade 9

Theory

 Number Base Systems

Decimal

Binary

Ternary

Oct.

Hex.

0

0

0

0

0

1

1

1

1

1

2

10

2

2

2

3

11

10

3

3

4

100

11

4

4

5

101

12

5

5

6

110

20

6

6

7

111

21

7

7

8

1000

22

10

8

9

1001

100

11

9

10

1010

101

12

A

11

1011

102

13

B

12

1100

110

14

C

13

1101

111

15

D

14

1110

112

16

E

15

1111

120

17

F

16

10000

121

20

10

17

10001

122

21

11

18

10010

200

22

12

19

10011

201

23

13

20

10100

202

24

14

Solutions from the Previous Issue:

Find y from the following equations:

  1. y3 = 27

        Solution: y3 = 27; y=3      

  1. (2)3 2y 2-7 = -1

        Solution: (2)3 2y 2-7 = -1; 3 + y - 7= 0; y 4 = 0; y = 4;

Simplify:

Solution: = =

  1. (4x3)2

        Solution: (4x3) 2 = 16x6

        Solution: =

Proposed Exercises: 

  1. How many different coin combinations could a person have if she has exactly 21 cents?
  2. In the movie Tandem, a character explains that the number on his car's odometer, 83238, is a palindrome, since it reads the same from left to right as from right to left. He then remarks that the next palindrome will be 83338. What number is the seventh palindrome after 83338?
  3. The pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd letter in the pattern?
  4. Without using a calculator or computer, determine which is larger, 23000 or 32000.
  5. If a and b are positive integers, neither of which is divisible by 10, and if ab = 10,000, find the sum a + b.