Brief description of number systems and exercises. Taken from the book Problem solving through recreational mathematics.

1. Mtro. Edgar Sánchez Linares

2. When the first Martian to visit Earth attended a high
school algebra class, he watched the teacher show
that the only solution of the equation 5x2-50x+125=0 is
x=5.
“How strange”, thougth the Martian. “On Mars, x=5 is
a solution of this equation, but there is also another
solution.”
If Martians have more fingers than humans have, how
many fingers do Martians have?
BonnieAverbach & Orin Chein

3. Ten symbols are required by our number
system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
The relative position to the decimal point
indicates the “place value” of the digit
3= 3x1 =3x100
30= 3x10 =3x101
300= 3x100 =3x102
0.3= 3 /10 =3x10-1
24=
204=
315=
45.2=

4. What if we have a number system with
only two different symbols?
0, 1
So, the number 1101 in base two
represents:
1 x23 +
How many symbols do we need in base
three? And the number 120 represents …
(110)two=
(110)three=
(110)ten=
(110)four=

5. (201)three=2x32+0x3+1=(19)ten
(1101)two=
(1001)seven=
(3.5)six=
(T81)eleven=
(5403)six=
(10011)two=
=(19)ten
(185)ten=(???)three
= 2 x 81 + (185-162)
= 2 x 81 + 23
= 2 x 81 + 2 x 9 +(23-18)
= 2 x 81 + 2 x 9 + 5
= 2 x 81 + 2 x 9 + 3 +2
= 2 x 34 + 0 x 33 +
+2 x 32+ 1 x 31 + 2 x 30
= (20212)three
Convert (2087)ten into each of
the following bases:
2, 3, 6, 7, 12

6. in other
bases