So, let’s count in base 6

• Digits allowed: 0, 1, 2, 3, 4, 5

• There is no such thing as 6

• When we read a number such as 2136, we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”

Count! In base 6• 1, 2, 3, 4, 5,• 10, 11, 12, 13, 14, 15,• 20, 21, 22, 23, 24, 25,• 30, 31, 32, 33, 34, 35,• 40, 41, 42, 43, 44, 45,• 50, 51, 52, 53, 54, 55,• 100, 101, 102, 103, 104, 105, 110

Compare base 6 to base 10

• Digits 0 - 9• New place value after 9

in a given place• Each place is 10 times

as valuable as the one to the right

• 243 = 2 • (10 • 10) + 4 • 10 + 3 • 1

• Digits 0 - 5• New place value after 5

in a given place• Each place is 6 times

as valuable as the one to the right.

• 243base 6 = 2 • (6 • 6) + 4 • 6 + 3 • 1or 99 in base 10

In base 6, write the first five place values.

_____ _____ _____ _____ _____

1296 216 36 6 1

64 63 62 61 60

cube flat long unit

Compare Base 6 to Base 10

312 =

3 • 100 +

1 • 10 + 2 • 1

312base 6 =

3 • 36 +

1 • 6 +

2 • 1 =

116 in base 10

How to change from Base 10 to Base 6.

• Suppose your number is 325 in base 10.• We need to know what our place values will

look like.• _____ _____ _____ _____

6•6•6 6•6 6 1

Now, 6•6•6 = 216. 216 = 1000 in base 6.

Base 10 to Base 6

• ___1__ _____ _____ _____ 6•6•6 6•6 6 1

• Now, 325 - 216 = 109. Since 109 is less than 216, we move to the next smaller place value: 6 • 6 = 36.

• 109 - 36 = 73. Since 73 is greater than 36, we stay with the same place value.

Base 10 to Base 6

• __1___ ___3__ _____ _____

6•6•6 6•6 6 1• We had 109: 109 - 36 - 36 - 36 = 1. We

subtracted 36 three times, so 3 goes in the 36ths place.

• We have 1 left. 1 is less than 6, so there are no 6s. Just a 1 in the units place.

Base 10 to Base 6

• __1___ ___3__ __0___ __1___

6•6•6 6•6 6 1

• Check: 1 • 216 + 3 • 36 + 1 • 1 = 325

Count! In base 16 1, 2, 3, 4, 5, 6, 7, 8, 9, a,

b, c, d, e, f

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f

20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f

In base 16, write the first five place values.

______ _____ _____ _____ _____

65,536 4096 256 16 1

164 163 162 161 160

In base 5, write the first five place values.

_____ _____ _____ _____ _____

625 125 25 5 1

54 53 52 51 50

cube flat long unit

In base 2, write the first five place values.

_____ _____ _____ _____ _____

16 8 4 2 1

24 23 22 21 20

Let’s Look at Adding and Subtracting in Alphabitia

• If we use the Alphabitian numerals, do our rules for addition and subtraction hold true?

• Warm up: tell me one more and one less of each• AB• CAD• B0B• AA0• DD• Use manipulatives or drawings to explain your

answers.

Let’s add in Alphabitia BCD

+ DB

BCD is DB is BCD + DB is

You try:

B0B+ABC

Use the manipulatives or draw pictures to help explain your answer.

Let’s subtract

CBD- ADC =

CBD is ADC is CBD - ADC is

You Try…

D00-B0B

B0A-BD

You try: Use manipulatives or drawings to explain

BBC - A0C

A0A0D - BCA

First Exam Scheduled• Wednesday, February 13th• Cover material from: • Textbook: 1.2, 1.3, 1.4, 1.7, 2.3, 3.1, 3.2• Explorations: 1.1, 1.4, 1.7, 2.8, 2.9, 3.1, 3.6• Notes/Problems from class• Sample test questions on line next Monday.

Homework for Monday• Exploration 2.9:

Part 1: for Base 6, 2, and 16, do #2; Part 3: #2, 3; Part 4: #1, 2, 4.

• Read Textbook pp. 109-118 • Do Textbook Problems pp. 120 - 121:

15b,c, 16b,d, 17a,i, 18b,f, 19, 29