Question:

Problem H1 Write the base five numbers 1234_five and 1.234_five as base ten numbers.

Problem H2 Find the base ten fractions represented by the following: a.a. 0.1_five, 0.2_five, 0.3_five, and 0.4_five b.b. 0.01_five, 0.02_five, 0.03_five, and 0.04_five c.c. 0.12_five, 0.23_five, 0.34_five, 0.43_five

Problem H3 Find the base five representation for these base ten fractions: a.9/25 b.23/125

Problem H4 a.If you were counting in base five, what number would you say just before you said 100? b.In base five, what number is one more than 344? c.What is the greatest three-digit number that can be written in base five? What numbers come just before and just after this number?

Problem H5 What number in base five behaves the way 3 does in base four?

Problem H6 a.Count by twos to 30_five. b.In base five, how can you tell if a number is even? c.Count by threes to 30_five.

TAKE IT FURTHER

Problem H7 Find the base five representation for the base ten fraction 1/2.

Problem H8 How might you tell if a number is even or odd in bases two, three, four, five, six, seven, eight, nine, and ten? Can you generalize to base n?

Problem H9 In order to use base sixteen, we need 16 digits. However, we only know 10 digits 0, 1, 2, ... , 8, and 9 so to represent 10, 11, 12, 13, 14, and 15 in base sixteen, we'll use A, B, C, D, E, and F, respectively. This gives us the following representation for the base sixteen digits:

Digit		0		1		2		3		4		5		6		7		8		9		10		11		12		13		14		15
Base Sixteen Format		0		1		2		3		4		5		6		7		8		9		A		B		C		D		E		F

Remember that 16 in this base is written as 10 (one-zero). So, for example, the number A6_sixteenbecomes (10 16) + 6, or 166, in base ten. The number 123 in base ten is (7 16) + 11 , or 7B, in base sixteen.

Now translate these base sixteen numbers into base ten numbers:

a.6D_sixteen b.AE_sixteen c.9C_sixteen d.2B_sixteen

Problem H10 Using the same system, translate these base ten numbers into base sixteen numbers: a.97 b.144 c.203 d.890